Tasamo makes two types of vehicle – SUV and Pickup Truck. These vehicles require

Question

Tasamo makes two types of vehicle – SUV and Pickup Truck. These vehicles require three types of special materials: material A material B material C. Each SUV requires 30 pounds of material A, 20 pounds of material B, and 50 pounds of material C. Each Pickup Truck requires 30 pounds of material A, 40 pounds of material B, and 80 pounds of material C. The profit for each SUV is $3000 and the profit for each Pickup Truck is $5500. Due to suppliers' capacity limits, Tony can only obtain 6000 pounds of material A, 5000 pounds of material B, and 6500 pounds of material C per month. Tasamo also needs to produce at least 50 SUV per month to fulfill a contract. Tasamo wants to find a production plan (i.e., the number of SUV and Pickup Truck to make) to maximize his monthly profit. Let x be the number of SUV to make per month. Let y be the number of Pickup Truck to make per month. Tasamo has formulated this decision problem as a linear program and solved it with Excel Solver. Tasamo obtained the following report from Excel Solver. s2.png Use the report to answer the following questions. A) What is the maximum profit at the optimal solution? B) Suppose the profit per SUV becomes $2700 per vehicle, should Tasamo change the production plan? [Type Yes or No in the blank.] C) If Tasamo can get 100 more pounds of Material B per month, how much would the objective function value change?

Explanation / Answer

An optimal solution is a feasible solution where the objective function reaches its maximum(or minimum)value.for example the most profit or the least cost.

from given problem

A B C

30 20 50 SUV 3000 X

30 40 80 PIC 5500 Y

6000 5000 6500

the A profit for SUV is 30*3000=30000

actually this is the profit for month30=30000

for 1day 30000/30

3000

the b's profit for SUV is 20*3000=60000

this is for 1 month 30=60000

then for one day=60000/30=2000

the c's profit for SUV is 50*3000=150000

this is for 1 month then for 1 day

30=150000

1=150000/30=5000

for A's profit on PIC is 30*5500=165000

for 30 days 165000

for 1 day 165000/30=5500

for B's profit PIC is 40*5500=220000

for 30 days 220000

for 1 day7333

for c's profit for PIC is 80*5500=440000

then for 30 days 440000

for 1 day=14666

for A 3000+5500=8500

for B 2000+7333=9333

for C 5000+14666=9666

then they give to tony

A is8500-6000=2500 remaining

B is 9333-5000=4333

C is 9666-6500=3166

optimal solution for 50 is 50*3000=1500000

the optimal soltion is 1500000-37499=112501

B) yes

C)160*5000=800000

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