{"id":23172,"date":"2022-01-05T23:52:36","date_gmt":"2022-01-05T23:52:36","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/a-company-manufactures-two-products-x-and-y-each-product-has-to-be\/"},"modified":"2022-01-05T23:52:36","modified_gmt":"2022-01-05T23:52:36","slug":"a-company-manufactures-two-products-x-and-y-each-product-has-to-be","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/a-company-manufactures-two-products-x-and-y-each-product-has-to-be\/","title":{"rendered":"A company manufactures two products x and y. each product has to be"},"content":{"rendered":"
\n

A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 hours respectively. The employee hours available in a month are 1,500 for the welding department, 1,500 in assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y.\u00a0<\/span><\/span><\/span><\/p>\n

1. Which one is one of the decision variables for this problem?\u00a0<\/span><\/span><\/span><\/p>\n

a. X: Hours spent for product X\u00a0<\/span><\/span><\/span><\/p>\n

b. X: Quantity to be produced for product X\u00a0<\/span><\/span><\/span><\/p>\n

c. X: Profit (contribution) margin for product X\u00a0<\/span><\/span><\/span><\/p>\n

d. None\u00a0<\/span><\/span><\/span><\/p>\n

2. Total profits are maximized when the objective function (as a straight line on a graph) is:\u00a0<\/span><\/span><\/span><\/p>\n

a. Nearest to the origin irrespective of the \u2018feasible region\u2019\u00a0<\/span><\/span><\/span><\/p>\n

b. Nearest to the origin and tangent to the \u2018feasible region\u2019\u00a0<\/span><\/span><\/span><\/p>\n

c. Furthest from the origin and tangent to the \u2018feasible region\u2019\u00a0<\/span><\/span><\/span><\/p>\n

d. Furthest from the origin irrespective of the \u2018feasible region\u2019\u00a0<\/span><\/span><\/span><\/p>\n

3. What is the equation of the labor constraint line for the welding department in this linear model?<\/span><\/span><\/span><\/p>\n

a. 2X + 3Y = 1,500 hours\u00a0<\/span><\/span><\/span><\/p>\n

b. 3X + 2Y = 550 hours\u00a0<\/span><\/span><\/span><\/p>\n

c. 2X + 3Y = 550 hours\u00a0<\/span><\/span><\/span><\/p>\n

d. 3X + 2Y = 1,500 hours\u00a0<\/span><\/span><\/span><\/p>\n

4. What is the solution to this linear programming problem in terms of the respective quantities of X and Y to be produced if profits are to be maximized?\u00a0<\/span><\/span><\/span><\/p>\n

a. X = 0, Y = 500\u00a0<\/span><\/span><\/span><\/p>\n

b. X = 150, Y = 400\u00a0<\/span><\/span><\/span><\/p>\n

c. X = 400, Y = 150\u00a0<\/span><\/span><\/span><\/p>\n

d. X = 550, Y = 0\u00a0<\/span><\/span><\/span><\/p>\n

e. None\u00a0<\/span><\/span><\/span><\/p>\n

5. Which resource (constraint) is not bounding the feasible region?\u00a0<\/span><\/span><\/span><\/p>\n

a. Welding\u00a0<\/span><\/span><\/span><\/p>\n

b. Assembly\u00a0<\/span><\/span><\/span><\/p>\n

c. Paint\u00a0<\/span><\/span><\/span><\/p>\n

d. All Bounding\u00a0<\/span><\/span><\/span><\/p>\n

\u00a0<\/p>\n

6. Welding, Assembly, and Paint availability hours are extended by 10% (added overtime) and problem is solved again. Following screen shot shows the MS Excel solver solution after this change. What is the value of Objective (Z)?\u00a0<\/span><\/span><\/span><\/p>\n

a. 65,000\u00a0<\/span><\/span><\/span><\/p>\n

b. 66,300\u00a0<\/span><\/span><\/span><\/p>\n

c. 67,600\u00a0<\/span><\/span><\/span><\/p>\n

d. 68,900\u00a0<\/span><\/span><\/span><\/p>\n

e. 69,300\u00a0<\/span><\/span><\/span><\/p>\n

7. Utilizing the initial given data if management wants to increase the profit more what would you recommend?\u00a0<\/span><\/span><\/span><\/p>\n

a. Increase available hours for Welding\u00a0<\/span><\/span><\/span><\/p>\n

b. Increase available hours for Paint\u00a0<\/span><\/span><\/span><\/p>\n

c. Reduce hours needed to weld for X and\/or Y\u00a0<\/span><\/span><\/span><\/p>\n

d. All above can be proposed\u00a0<\/span><\/span><\/span><\/p>\n

e. None of these can be proposed\u00a0<\/span><\/span><\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 hours […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-23172","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/23172","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=23172"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/23172\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=23172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=23172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=23172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}