{"id":7656,"date":"2021-10-13T23:11:50","date_gmt":"2021-10-13T23:11:50","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/the-emergency-room-at-hsi-serves-patients-who-arrive-according-to-a\/"},"modified":"2021-10-13T23:11:50","modified_gmt":"2021-10-13T23:11:50","slug":"the-emergency-room-at-hsi-serves-patients-who-arrive-according-to-a","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/the-emergency-room-at-hsi-serves-patients-who-arrive-according-to-a\/","title":{"rendered":"The emergency room at hsi serves patients who arrive according to a"},"content":{"rendered":"
\n

Hospital Systems, Inc (HSI)<\/span><\/p>\n

The emergency room at HSI serves patients who arrive according to a Poisson distribution at the rate of 9 per hour.\u00a0 Treatment takes an average of 6 minutes and the treatment times can be considered to follow an exponential distribution.\u00a0 What is the<\/span><\/p>\n

(a)\u00a0 minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately?<\/span><\/p>\n

(b)\u00a0 minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised?\u00a0 No more than 15 minutes?<\/span><\/p>\n

Broke & Down Machine Shop<\/span><\/p>\n

Broke & Down has several hundred machines in its large manufacturing facility as it uses the PWP concept (plant-within-a-plant).\u00a0 Ray Pear, Manager of Maintenance and Chief Mechanic for the Broke & Down Machine Shop, says that broken machines arrive at the repair facility according to a Poisson pattern at the average rate of 2 per 8-hour day.\u00a0 Ray likes to remind his boss, Mr. I. M. Broke, that since he is such a master mechanic he is the only person needed to repair the broken machines, and he can repair a machine in just 2 hours on average.\u00a0 Furthermore, the repair time follows an exponential distribution, and Ray repairs the machines in the order in which they break down.\u00a0 Assuming that the machine shop operates 8 hours per day:<\/span><\/p>\n

(a)\u00a0 if a machine breaks down, what is the probability that Ray can begin work on it immediately?<\/span><\/p>\n

(b)\u00a0 on average, how long is a broken machine out of service?<\/span><\/p>\n

(c)\u00a0 on average, how many machines are awaiting repair?<\/span><\/p>\n

(d) Mr. Churchill Down, co-owner of the machine shop is concerned that too much productive time is being lost due to machine break downs.\u00a0 He agrees that Ray is a super mechanic but also thinks that Ray needs help so the shop would have less downtime waiting for repairs.\u00a0 Churchill knows of Ray\u2019s son Desmond, often called Des for short.\u00a0 Des is also a master mechanic and Churchill has been considering hiring Desmond for some time if it is economically feasible.\u00a0 Master mechanics are paid $20 per hour, and the machines produce revenue at $60 per hour when in service.\u00a0 Should Des Pear be hired?<\/span><\/p>\n

(e)\u00a0 I. M. Broke is not too keen on the idea of hiring Des Pear as it has a flavor of nepotism.\u00a0 I. M. suggests that to help Ray they could invest in more sophisticated diagnostic equipment and repair tools that would reduce Ray\u2019s average repair time to 1 hour and 20 minutes (i.e. 4\/3 hours).\u00a0 If these more sophisticated tools and equipment cost Broke & Down $20 per hour to operate, and Ray is paid $20 per hour, should the investment be made?\u00a0 Again, the machines produce revenue at the rate of $60 per hour when in service.<\/span><\/p>\n

(f)\u00a0 Anna Last, Director of Corporate Analytics for Broke & Down suggests that the use of the more sophisticated equipment (part e) not only shortens the average repair time but also the associated variability and changes the distribution of the repair time so it is no longer exponential.\u00a0 From discussions with the manufacturer of the equipment, it is estimated that the standard deviation of the repair time is 1 hour.\u00a0 Does this change what I.M. should do?\u00a0 Show\/explain.<\/span><\/p>\n

City Cab, Inc.<\/span><\/span><\/p>\n

City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs.\u00a0 The telephone calls that are made to City Cab use a common telephone number.\u00a0 When both dispatchers are busy, the caller hears a busy signal; no waiting is allowed.\u00a0 Callers who receive a busy signal can call back later or call another cab company for service.\u00a0 Assume that the arrival of calls follows a Poisson distribution, with a mean of 40 calls per hour, and that the call handling time follows an exponential probability distribution with a mean service time of 2 minutes.\u00a0 Based on this information, answer the following questions.<\/span><\/p>\n

What percentage of the time are both dispatchers idle?<\/span><\/p>\n

What percentage of the time are both dispatchers busy?<\/span><\/p>\n

What is the probability that a caller will receive a busy signal if 2, 3, or 4 dispatchers are used?<\/span><\/p>\n

If management wants no more than 12% of the callers to receive a busy signal, how many dispatchers should be used?<\/span><\/p>\n

Suppose the service time distribution is not exponential, it follows some other distribution such as a normal, but the mean service time remains at 2 minutes.\u00a0 Does this make any difference in the model used and in the results?\u00a0 Explain.<\/span><\/p>\n

\u00a0<\/span><\/p>\n

Nooner Appliance<\/span><\/p>\n

1.\u00a0\u00a0 Nooner Appliance Producers (NAP), a small appliance manufacturing company that specializes in clocks, must decide what types and quantities of output to manufacture for each week\u2019s sale.\u00a0 Currently Nooner makes only two kinds of clocks, regular clocks and alarm clocks, from which the product mix is selected.\u00a0 Next week\u2019s product mix can only be produced with the labor, facilities, and parts currently on hand.\u00a0 These supplies are as follows:<\/span><\/p>\n

Number of labor hours\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1,600<\/span><\/p>\n

Number of processing hours\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1,800<\/span><\/p>\n

Number of alarm assemblies\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 350<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 The resources are related to the two alternative manufactured outputs, regular clocks and alarm clocks, in the following way:\u00a0 each regular clock produced requires 2 hours of labor and 6 hours of processing, while each alarm clock produced requires 4 hours of labor and 2 hours of processing.\u00a0 The profit per unit for regular clocks is $3.00 while the company makes $8 per unit for alarm clocks.\u00a0 Additionally, at least 300 clocks in total must be produced.\u00a0 How many of each type of clock should Nooner produce to maximize profit? \u00a0The LP structure and solution are shown below.\u00a0<\/span><\/p>\n

LINEAR PROGRAMMING PROBLEM:\u00a0 Nooner Appliance Producers (NAP)<\/span><\/p>\n

MAX 3X1+8X2<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 S.T.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1)\u00a0 2X1+4X2<1600<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2)\u00a0 6X1+2X2<1800<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3)\u00a0 1X2<350<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4)\u00a0 1X1+1X2>300<\/span><\/p>\n

OPTIMAL SOLUTION<\/span><\/p>\n

Objective Function Value =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3100.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 Variable\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Value\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Reduced Costs\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0 ————–\u00a0\u00a0\u00a0\u00a0 —————\u00a0\u00a0\u00a0\u00a0\u00a0 ——————<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 100.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 350.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 Constraint\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Slack\/Surplus\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Dual Prices\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0 ————–\u00a0\u00a0\u00a0\u00a0 —————\u00a0\u00a0\u00a0\u00a0\u00a0 ——————<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.500<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 500.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 150.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.000<\/span><\/p>\n

\u00a0<\/span><\/p>\n

OBJECTIVE COEFFICIENT RANGES<\/span><\/p>\n

\u00a0\u00a0 Variable\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lower Limit\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Current Value\u00a0\u00a0\u00a0\u00a0 Upper Limit<\/span><\/p>\n

\u00a0————\u00a0\u00a0 —————\u00a0\u00a0\u00a0 —————\u00a0 —————<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 X1\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a00.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 X2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8.000\u00a0\u00a0 No Upper Limit<\/span><\/p>\n

RIGHT HAND SIDE RANGES<\/span><\/p>\n

\u00a0 Constraint\u00a0\u00a0\u00a0\u00a0\u00a0 Lower Limit\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Current Value\u00a0\u00a0\u00a0\u00a0 Upper Limit<\/span><\/p>\n

\u00a0————\u00a0\u00a0 —————\u00a0\u00a0\u00a0 —————\u00a0 —————<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1400.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1600.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1766.667<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1300.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1800.000\u00a0\u00a0 No Upper Limit<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 300.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 350.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 400.000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 No Lower Limit\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 300.000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 450.000<\/span><\/p>\n

Given the Nooner\u00a0 scenario:<\/span><\/p>\n

(a)\u00a0\u00a0\u00a0\u00a0 Solve using the graphical solution procedure and identify all extreme points of the feasible region.\u00a0<\/span><\/p>\n

(b) \u00a0\u00a0\u00a0 How much of each clock should be produced and what is the associated profit??<\/span><\/p>\n

Using the output from the Management Scientist, answer the remaining questions.<\/span><\/p>\n

(c)\u00a0\u00a0\u00a0\u00a0 What are the values and interpretations of all slack and surplus variables?<\/span><\/p>\n

(d)\u00a0\u00a0\u00a0 Determine (compute manually) and interpret the range of optimality for the objective function coefficients.<\/span><\/p>\n

(e)\u00a0\u00a0\u00a0\u00a0 Interpret each of the shadow prices.<\/span><\/p>\n

(f)\u00a0\u00a0\u00a0\u00a0 If the profit on an alarm clock decreased to $6 per unit, what parts of the optimal solution would change and how, and what parts would not change?\u00a0 Explain your rationale.<\/span><\/p>\n

(g)\u00a0\u00a0\u00a0\u00a0 Suppose Nooner can get an additional 100 alarm assemblies at a premium price of $1 more than the current price.\u00a0 Should Nooner take advantage of this offer?\u00a0\u00a0 Explain your rationale.<\/span><\/p>\n

\u00a0<\/span><\/p>\n

Monroe County Sheriff<\/span><\/p>\n

The Monroe County Sheriff\u2019s Department schedules police officers for 8-hour shifts.\u00a0 The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m.\u00a0 An officer beginning a shift at one of these times works for the next eight hours.\u00a0 During normal weekday operations, the number of officers needed varies depending on the time of the day.\u00a0 The department staffing guidelines require the following minimum number of officers on duty:<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Time of Day\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Minimum Officers on Duty<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8:00 a.m. – noon\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 5<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Noon – 4:00 p.m.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 6<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4:00 p.m. – 8:00 p.m.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8:00 p.m. – midnight\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 7<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Midnight – 4:00 a.m.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 4<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4:00 a.m. – 8:00 a.m.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 6<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 How many police officers should be scheduled to begin the 8-hour shifts at each of the six times in order to minimize the total number of officers required?\u00a0 Structure this linear programming problem (decision variables, objective function, and constraints).\u00a0 You do not need to solve this problem, just structure it.<\/span><\/p>\n

Chase Shipping<\/span><\/p>\n

Sean Skippers is in charge of load planning for cargo ships for Chase Shipping Inc. (CSI).\u00a0 Sean is preparing a load plan for a CSI freighter destined for China.\u00a0 An agricultural commodities dealer would like to transport three commodity products aboard this ship.\u00a0 The shipping characteristics of these commodities are shown below.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Amount\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Volume per Ton\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Profit per Ton<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Commodity\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Available (tons)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (cubic feet)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ($)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4800\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 40\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 70<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 50<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2900\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 60\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 80<\/span><\/p>\n

Sean can elect to load any and\/or all of the available commodities.\u00a0 However, the ship has three cargo holds with the following capacity restrictions:<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Cargo Hold\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Weight Capacity (tons)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Volume Capacity (cubic feet)<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Forward\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 145,000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Center\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 180,000<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Rear\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 155,000<\/span><\/p>\n

More than one type of commodity can be placed in the same cargo hold.\u00a0 However, because of balance considerations, the weight in the forward cargo hold must be within\u00a0<\/span>+<\/span><\/span>\u00a010% of the weight in the rear cargo hold.\u00a0 Structure as a linear programming problem (decision variables, objective function, and constraints).\u00a0 You do not need to solve this problem, just structure it.<\/span><\/p>\n

EPC<\/span><\/p>\n

The executives of Electronic Products Company (EPC) have to decide which of two products to introduce, A or B.\u00a0 Each has been in the R&D process for about 4 years and the company feels that they are now ready for introduction.\u00a0 Additionally, considerable market research has been done to assses the market for each product.\u00a0 Each of these new products is expected to have a five year life before renewal or phase-out.<\/span><\/p>\n

Product A is essentially a lower risk proposition.\u00a0 For this product, market research has made estimates of likely market sizes and profitability as follows:\u00a0 Sales may be high, with a resulting profit of $10 million, medium with a net profit of $5 million, or low, in which case the company just breaks even.\u00a0 The probabilities for these outcomes are respectively, 0.50, 0.20, and 0.30.<\/span><\/p>\n

Product B is a little more risky in that the plant size has to be matched to the demand for the product.\u00a0 There are two key decisions to be made which deal with plant size, namely, the initial size and the final size.\u00a0 The possibilities for the initial and final size are either small or large as demand could be either low or high initially.\u00a0 Follow-on demand could also be low or high but it is possible that demand changes so that a low initial demand could eventually become high and a high initial demand could eventually sharply drop to a low volume.\u00a0 The initial plant size will be for the first two years, at which point a decision has to be made on whether to expand the plant if demand exceeds capacity.\u00a0 The additional cost of a plant expansion is $1.0 million.\u00a0 If a large plant is initially built, then there is no need to expand but it is difficult to downsize the plant.\u00a0 If the plant is initially too small to meet demand, lost sales and unhappy customers will be the result but the plant can be expanded after two years to alleviate the situation.\u00a0 However, if the plant has too much excess capacity, then profitability is greatly reduced and some losses become a possibility.\u00a0 The probability of initial sales being low or high is 0.4 and 0.6 respectively.\u00a0 The likelihood of follow-on sales being low or high is dependent somewhat on initial sales and is shown below along with the corresponding profitability.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Probability Analysis for Product B<\/span><\/span><\/p>\n

Initial Sales\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Follow-on Sales (Years 3-5)<\/span><\/p>\n

(First 2 Years)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Low\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 High\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Low\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.60\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.40<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 High\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.30\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.70<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

The Corporate Financial Analysis Division, working with Sales and Marketing, has come up with the following profitability estimates for Product B based on the possible scenarios.\u00a0 The total profit for the 5-year planning period would be the profit made in the first two years plus that made in years 3-5. The estimated cost of the plant expansion ($1.0 million) is not included in these figures.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Profit Table ($ in Millions)<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Years 1-2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Years 3-5<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Low Demand\u00a0\u00a0\u00a0\u00a0 High Demand\u00a0\u00a0\u00a0 Low Demand\u00a0\u00a0\u00a0\u00a0 High Demand<\/span><\/p>\n

\u00a0Small Plant\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 1.0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 2.0<\/span><\/p>\n

\u00a0 Large Plant\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1.0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5.0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -2.0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10.0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

(a)\u00a0\u00a0\u00a0\u00a0 Which product should EPC introduce?\u00a0 (show work\/analysis)<\/span><\/p>\n

(b)\u00a0\u00a0\u00a0\u00a0 Create a risk profile for EPC.\u00a0<\/span><\/p>\n

(c)\u00a0\u00a0\u00a0\u00a0 How risky is EPC\u2019s best solution?<\/span><\/p>\n

(d)\u00a0\u00a0\u00a0 Suppose the CEO of EPC has reservations about your analysis of his key decision on new product introduction.\u00a0 He wants to know if there is a way to account for his view of risk and how he would make some of the decisions other than just EMV.\u00a0 Explain what you would have to do to satisfy his fears.<\/span><\/p>\n

\u00a0<\/p>\n

\u00a0<\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Hospital Systems, Inc (HSI) The emergency room at HSI serves patients who arrive according to a Poisson distribution at the rate of 9 per hour.\u00a0 Treatment takes an average of 6 minutes and the treatment times can be considered to follow an exponential distribution.\u00a0 What is the (a)\u00a0 minimum number of doctors required so that […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7656","post","type-post","status-publish","format-standard","hentry","category-homework-help"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/7656","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=7656"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/7656\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=7656"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=7656"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=7656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}