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Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (You may use QM-software for this problem. All the detailed output should be displayed). a) Formulate this as a linear programming problem. Carefully define all decision variables. b) Show the graph of the feasible region indicating all the relevant corner points c) Find the optimal solution to this LP and find the maximum profits.

Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (You may use QM-software for this problem. All the detailed output should be displayed). a) Formulate this as a linear programming problem. Carefully define all decision variables. b) Show the graph of the feasible region indicating all the relevant corner points c) Find the optimal solution to this LP and find the maximum profits.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 89P
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ythos.content.blackboardcdn.com/5c1c67a3c99fc/2929686?X-Blackboard-Expiration=D1606219200000&X 1/ 1 QUESTION 1 Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (You may use QM-software for this problem. All the detailed output should be displayed). a) Formulate this as a linear programming problem. Carefully define all decision variables. b) Show the graph of the feasible region indicating all the relevant corner points c) Find the optimal solution to this LP and find the maximum profits. QUESTION 2 A community farm has 6000 square kilometers of land available to plant wheat and millet. Each kilometer square of wheat requires 9 gallons of fertilizer and insecticide and 4 hour of labor to harvest. Each square kilometer of millet requires 3 gallons of fertilizer and insecticide and 1 hour of labor to harvest. The community has at most 40,500 gallons of fertility and insecticide and at most 5250 hours of labor for harvesting. If the profits per square kilometer are $60 for wheat and $40 for millet, how many square kilometers of each crop should the community plant in order to maximize profits? What is the maximum profit? Hint: x is the number of square kilometers of wheat and y is the number of square kilometers of millet. (A complete solution is required for this problem - No software) a
Transcribed Image Text:ythos.content.blackboardcdn.com/5c1c67a3c99fc/2929686?X-Blackboard-Expiration=D1606219200000&X 1/ 1 QUESTION 1 Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (You may use QM-software for this problem. All the detailed output should be displayed). a) Formulate this as a linear programming problem. Carefully define all decision variables. b) Show the graph of the feasible region indicating all the relevant corner points c) Find the optimal solution to this LP and find the maximum profits. QUESTION 2 A community farm has 6000 square kilometers of land available to plant wheat and millet. Each kilometer square of wheat requires 9 gallons of fertilizer and insecticide and 4 hour of labor to harvest. Each square kilometer of millet requires 3 gallons of fertilizer and insecticide and 1 hour of labor to harvest. The community has at most 40,500 gallons of fertility and insecticide and at most 5250 hours of labor for harvesting. If the profits per square kilometer are $60 for wheat and $40 for millet, how many square kilometers of each crop should the community plant in order to maximize profits? What is the maximum profit? Hint: x is the number of square kilometers of wheat and y is the number of square kilometers of millet. (A complete solution is required for this problem - No software) a
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