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 College Park Motor's marketing consultant has come up with the following demand curves: SU'v" demand = 400 0.014[SU'v' price] + 0.003(wagon price] Wagon demand = 425 0.010{wagon price} + 0.005(5U'v' price} [The demand curve accounts for interactions. For example, if wagon price goes up Wagon demand will fall and some of that demand will instead switch to SU'v's.] The dealership's unit costs are 511,000 for 50'st and $14,000 for wagons. Each SLI'v' 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 SU'v's and wagons. [It is okay for prices andfor 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 mode] make sure to write out the algebraic equivalent of your model. b. Implement your model from part a in Solver. Document your model appropriately so it is possible to identify the decision variables, objective function, and constraints without going into Solver. Make sure to paste the Solver dialog box into your spreadsheet. c. 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