Spencer Motors sells automobiles and trucks. The firm makes a $280 profit for each automobile it sells and a $375 profit for each truck it sells. The company is planning next quarter's order. The manufacturer says Spencer cannot order more than 300 trucks. They also limit the number of autos Spencer can order to a maximum of 400. Spencer requires 1.50 hours to prepare each auto and 3 hours to prepare each truck before it can be sold. Next quarter, the company will have 1500 hours of shop time available for preparation of new vehicles.
|
Processing Time
|
Max Order Quantity
|
Profit
|
|
Automobile
|
1.50
|
400
|
$ 280
|
|
Trucks
|
3
|
300
|
$ 375
|
|
Total Available
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1500
|
|
|
How many automobiles and trucks should Spencer order if they want to maximize their total profit?
(A) Clearly and completely define your decision variables.
(B) Formulate this problem as a linear programming model. Be sure to include the objective function and all relevant constraints.
(C) Use your favorite method to solve this problem and tell me what the optimal solution is and what the value of the objective function is at this point.
(D) Which constraints are binding? Why are they binding?