{"id":6887,"date":"2021-10-11T07:04:49","date_gmt":"2021-10-11T07:04:49","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/week-6-homework-questions-below-in-description\/"},"modified":"2021-10-11T07:04:49","modified_gmt":"2021-10-11T07:04:49","slug":"week-6-homework-questions-below-in-description","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/week-6-homework-questions-below-in-description\/","title":{"rendered":"Week 6 homework questions below in description"},"content":{"rendered":"
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\u00a0<\/span><\/span><\/span>MAT540 <\/span><\/strong>\u00a0<\/span>Quantitative Methods<\/strong><\/span><\/span><\/p>\n

\u00a0<\/span>Week 6 Homework <\/strong>\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Chapter 2 <\/strong><\/span><\/span><\/p>\n

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1. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Product 1 requires 10 hours of processing time on line 1 and product 2 requires 14 hours of processing on line 1. , On line 2, product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit. <\/span><\/span><\/p>\n

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

a. Formulate a linear programming model for this problem. <\/span><\/span><\/p>\n

b. Solve the model by using graphical analysis. <\/span><\/span><\/p>\n

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

2. The Pinewood Furniture Company produces chairs and tables from two resources \u2013 labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem. <\/span><\/span><\/p>\n

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

a. Formulate a linear programming model for this problem. <\/span><\/span><\/p>\n

b. Solve the model by using graphical analysis. <\/span><\/span><\/p>\n

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

3. In Problem 2, how much labor and wood will be unused if the optimal numbers of chairs and tables are produced? <\/span><\/span><\/p>\n

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

4. The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units and one gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required and the ingredients contribute 1 unit each per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost. <\/span><\/span><\/p>\n

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

a. Formulate a linear programming model for this problem. <\/span><\/span><\/p>\n

b. Solve the model by using graphical analysis. <\/span><\/span><\/p>\n

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

5. A clothier makes coats and slacks. The two resources required are wool cloth and labor. The <\/span><\/span><\/p>\n

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

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

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

clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is $50, and the profit for slacks is $40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized. <\/span><\/span><\/p>\n

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

a. Formulate a linear programming model for this problem. <\/span><\/span><\/p>\n

b. Solve the model by using graphical analysis. <\/span><\/span><\/p>\n

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

6. Solve the following linear programming model graphically: <\/span><\/span><\/p>\n

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

Maximize Z = 5x<\/span>1 <\/span>+ 8x<\/span>2 <\/span><\/span><\/p>\n

Subject to <\/span><\/span><\/p>\n

4x<\/span>1 <\/span>+ 5x<\/span>2 <\/span>\u2264 50 <\/span><\/span><\/p>\n

2x<\/span>1 <\/span>+ 4x<\/span>2 <\/span>\u2264 40 <\/span><\/span><\/p>\n

x<\/span>1 <\/span>\u2264 8 <\/span><\/span><\/p>\n

x<\/span>2 <\/span>\u2264 8 <\/span><\/span><\/p>\n

x<\/span>1<\/span>, x<\/span>2 <\/span>\u2265 0<\/span><\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u00a0MAT540 \u00a0Quantitative Methods \u00a0Week 6 Homework \u00a0\u00a0\u00a0\u00a0 \u00a0Chapter 2 \u00a0 \u00a0 1. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Product 1 requires 10 hours of processing time on line 1 and product 2 requires 14 […]<\/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-6887","post","type-post","status-publish","format-standard","hentry","category-homework-help"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/6887","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=6887"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/6887\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=6887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=6887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=6887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}