kindly answer items (d), (e), and (f)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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kindly answer items (d), (e), and (f)

Hondazuki manufactures cars and trucks. Each car contributes 300S to profit and each truck
contributes 400$. The resources required in manufacturing cars and trucks are shown on the table below. Each
day, Hondazuki can rent up to 98 Type 1 machines at 50$ per machine. At present, the company has 73 Type 2
machines and 260 tons of steel available. Marketing considerations dictate that at least 44 cars must be produced.
How many Type 1 machines should be rented daily and how many cars and trucks should be produced to
maximize the company's profit?
Days on Type 1 Machine
Days on Type 2 Machine
Tons of steel
Car
0.8
0.6
2
Truck
1.0
0.7
3
a. Formulate the problem into an LP in symmetric form.
b. Solve the LP and give the optimal tableau. You may use any software that can solve LP problems. (Hint:
Optimal profit is 32600S)
c. If the contribution to profit of each car produced is changed from 300S to 330S, will the current solution
remain optimal? If not, what is the new optimal solution? Show your manual computations.
d. What is the highest fee that Hondazuki should be willing to pay for the rent of Type 1 machine for 1 day?
e. What is the most that Hondazuki should be willing to pay for an extra ton of steel?
f. Hondazuki is considering of producing jeeps. A jeep contributes $600 to profit, requires 1.2 days on
machine 1 and wvill need 3 tons of steel. Should Hondazuki produce jeep? If yes, what will be the new
optimal solution and the optimal objective function value?
Transcribed Image Text:Hondazuki manufactures cars and trucks. Each car contributes 300S to profit and each truck contributes 400$. The resources required in manufacturing cars and trucks are shown on the table below. Each day, Hondazuki can rent up to 98 Type 1 machines at 50$ per machine. At present, the company has 73 Type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 44 cars must be produced. How many Type 1 machines should be rented daily and how many cars and trucks should be produced to maximize the company's profit? Days on Type 1 Machine Days on Type 2 Machine Tons of steel Car 0.8 0.6 2 Truck 1.0 0.7 3 a. Formulate the problem into an LP in symmetric form. b. Solve the LP and give the optimal tableau. You may use any software that can solve LP problems. (Hint: Optimal profit is 32600S) c. If the contribution to profit of each car produced is changed from 300S to 330S, will the current solution remain optimal? If not, what is the new optimal solution? Show your manual computations. d. What is the highest fee that Hondazuki should be willing to pay for the rent of Type 1 machine for 1 day? e. What is the most that Hondazuki should be willing to pay for an extra ton of steel? f. Hondazuki is considering of producing jeeps. A jeep contributes $600 to profit, requires 1.2 days on machine 1 and wvill need 3 tons of steel. Should Hondazuki produce jeep? If yes, what will be the new optimal solution and the optimal objective function value?
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