a) Let X is the no of Thrill seeker car and Y is the Classy Cruiser, profit per car is 3600 and 5400 respectively. One needs to maximize the function i.e.
Max (3600*X + 5400*Y)
The constraints are that the labor hours are restricted to 48000 and the no of doors are restricted to 20000. Also the maximum demand of Classy Cruiser is 3500. Keeping this constraints one solves the problem. Following is the output of the problem.
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Variables to be changed
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Family Thrill Seekers
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Classy Cruiser
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No of Cars to be produced
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3800
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2400
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Constraints
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Cars constraint total
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Company constraint
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Labour Hours
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6
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10.5
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48000
|
48000
|
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No of Doors
|
4
|
2
|
20000
|
20000
|
|
Limit on the cars
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|
2400
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2400
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3500
|
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|
|
|
|
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Objective function
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Total profit
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26640000
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b) Optimal solution gives 2400 Classy Cruiser to be produced even when the demand is 3500. So this is more than 20% of the cars that should be produced. So spending on advertisement is waste and will not affect the output as the constraint is a non binding.
c) Following is the solution if the no of labor hours are increased
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Variables to be changed
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Family Thrill Seekers
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Classy Cruiser
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|
No of Cars to be produced
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3250
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3500
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Constraints
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Cars constraint total
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Company constraint
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Labor Hours
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6
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10.5
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56250
|
60000
|
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No of Doors
|
4
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2
|
20000
|
20000
|
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Limit on the cars
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|
3500
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3500
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3500
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Objective function
|
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Total profit
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30600000
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d) Increase in profit by using extra 25%labor hours is 30600000 - 26640000 which equals to 3960000. So ideally this increase in profit should be the maximum cost which Rachel should be willing to shell out.
e) If the labor hour increases by 25% then the value becomes 60000 and similarly for the demand the value becomes 4200. Solving for these values one gets the following the answers:
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Variables to be changed
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Family Thrill Seekers
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Classy Cruiser
|
|
No of Cars to be produced
|
3000
|
4000
|
|
Constraints
|
Cars constraint total
|
Company constraint
|
|
Labor Hours
|
6
|
10.5
|
60000
|
60000
|
|
No of Doors
|
4
|
2
|
20000
|
20000
|
|
Limit on the cars
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|
4000
|
4000
|
4200
|
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Objective function
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Total profit
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32400000
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f) The increase in profit is 32400000- 26640000 = 5760000, so this is greater than the cost of advertising which is 500,000 and extra labor which is 1600000, the total is 2100000.
g) Following is the output of the solution
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Variables to be changed
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Family Thrill Seekers
|
Classy Cruiser
|
|
No of Cars to be produced
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1875
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3500
|
|
Constraints
|
Cars constraint total
|
Company constraint
|
|
Labor Hours
|
6
|
10.5
|
48000
|
48000
|
|
No of Doors
|
4
|
2
|
14500
|
20000
|
|
Limit on the cars
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|
3500
|
3500
|
3500
|
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Objective function
|
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Total profit
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24150000
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h) Following is the solution
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Variables to be changed
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Family Thrill Seekers
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Classy Cruiser
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|
No of Cars to be produced
|
1500
|
3500
|
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Constraints
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Cars constraint total
|
Company constraint
|
|
Labor Hours
|
7.5
|
10.5
|
48000
|
48000
|
|
No of Doors
|
4
|
2
|
13000
|
20000
|
|
Limit on the cars
|
|
3500
|
3500
|
3500
|
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Objective function
|
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Total profit
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24300000
|
i) In this one needs to modify one constraint. Instead of making the constraint for the cars as less than equal to one need to change the constraint to equal to 3500 cars. Following are the solutions
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Variables to be changed
|
| |
Family Thrill Seekers
|
Classy Cruiser
|
|
No of Cars to be produced
|
1875
|
3500
|
|
Constraints
|
Cars constraint total
|
Company constraint
|
|
Labor Hours
|
6
|
10.5
|
48000
|
48000
|
|
No of Doors
|
4
|
2
|
14500
|
20000
|
|
Limit on the cars
|
|
3500
|
3500
|
3500
|
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Objective function
|
|
Total profit
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25650000
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The decrease in profit if all the demands are met is equal to 25650000- 26640000 = 990000 which is less than the specified limit of 2000000. So one can produce 3500 Cruiser cars and meet all the required demand.
j) Following is the output
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Variables to be changed
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Family Thrill Seekers
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Classy Cruiser
|
|
No of Cars to be produced
|
2120
|
4200
|
|
Constraints
|
Cars constraint total
|
Company constraint
|
|
Labor Hours
|
7.5
|
10.5
|
60000
|
60000
|
|
No of Doors
|
4
|
2
|
16880
|
20000
|
|
Limit on the cars
|
|
4200
|
4200
|
4200
|
|
Objective function
|
|
Total profit
|
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28616000
|
The profit finally obtained will be 28616000 - advertising cost and overtime labor cost. So the profit is 28616000 -500000-1600000 which is equal to 26516000