2) College Park Motors is a car dealership that specializes in the sales of sport utility vehicles and station wagons. Due to its reputation for quality and service, College Park Motors has a strong position in the regional market but demand is somewhat sensitive to price. After examining the new models Covington's marketing consultant has come up with the following demand curves:

SUV demand = 400 - 0.014(SUV price) Wagon demand = 425 - 0.018(wagon price)

The dealership's unit costs are $17,000 for SUVs and $14,000 for wagons. Each SUV requires 2 hours of prep labor, and each wagon requires 3 hours of prep labor. The current staff can supply 320 hours of labor.

College Park Motors would like to determine profit maximizing prices for SUVs and wagons. (It is okay for prices and/or demand to be fractional in this problem. Do not add integer restrictions.)

a. Write down an algebraic formulation of a nonlinear optimization model that maximizes College Park Motors profit. Document your algebraic model so that it is clear what the variables, constraints, and objective function mean. In the event you prefer to work in excel directly to build a Solver Model, that is fine. After you build your Solver model make sure to write out the algebraic equivalent of your model.

1. What is the maximum profit? What should the SUV price and Wagon price be set at? And what is the resulting demand?

d. Using the sensitivity report obtained from solving your model, determine the marginal value of dealer prep labor.