Campbell Motors Auto Dealership Specializes Sale Station Wagons Light Trucks Reputation Qu Q32195038

Campbell Motors is an auto dealership that specializes in thesale of station wagons and light trucks. Because of its reputationfor quality and service, Campbell has a strong position in theregional market, but demand remains sensitive to price. Whileevaluating the new models, Campbell’s marketing consultant has comeup with the following demand/sales response curves:

Truck Demand = 500 – 18(Truck Price in thousands)

Wagon Demand = 400 – 11 (Wagon Price in thousands)

The dealership’s unit costs are $20,000 for each truck and$25,000 for each wagon. Each truck requires 3 hours of prep labor,and each wagon requires 2 hours of prep labor. The current staffcan supply at most a total of 250 hours of prep labor for thewagons and trucks purchased.

In order to feel good about the environment, Campbell hasdecided that the vehicles sold by Campbell Motors will meet the EPAemissions limit for NOx. Thus, Campbell wants the average emissionsof NOx over the vehicles sold by Campbell Motors to be at most .07grams per mile. From company data Campbell knows that a truck emits.14 grams per mile and that a wagon emits .05 grams per mile.

Campbell must determine how many cars and trucks to purchase tomaximize his profit.

State the decisions to be made in Campbell’s problem, theobjective and the constraints in words using <=, >= or = inthe constraints. (Handwrite answer, 5 points)

Define your inputs algebraically as decision variables. Then,using your objective and constraints in part (a), formulateCampbell’s problem as an algebraic linear optimization model.(Handwrite answer, 5 points)

Construct an EXCEL model corresponding to your algebraic modelin part (b). (Hand in via Blackboard, 5 points)

Optimize your EXCEL model using Solver and give the AnswerReport. What is Campbell’s maximum profit? What prices shouldCampbell set for the trucks and wagons to maximize profit? How manytrucks and wagons should he sell? (Hand in via Blackboard, 5points)