Managerial Report

Using the formulas given in equations $(12\mathrm{.}8)$ and $(12\mathrm{.}9),$ develop an expression for the total profit contribution as a function of the price of cars and the price of light trucks. Assume the marginal cost for passenger cars is $15$ and the marginal cost for light trucks is $17.$

Using Excel Solver or LINGO, find the price for each car so that the total profit contribution is maximized.

Given the prices determined in Question $2,$ calculate the number of passenger cars sold and the fumber of light trucks sold.

Duplicate the spreadsheet in Figure $12\mathrm{.}18.$ Your spreadsheet should have formulas in cells D$3$:D$5$ and B$7$ and be able to calculate the harmonic $($CAFE$)$ average for any MPG rating and any number of vehicles in each category.

Again, assume that passenger cars get $30MPG$ and light trucks get $20MPG$ calculate the CAFE average for the fleet size from Question $3.$

If you do the calculation in Question $5$ correctly, the CAFE average of the fleet is $23\mathrm{.}57.$ Add a constraint that the fleet average must be $25MPG$ and resolve the model to get the maximum total profit contribution subject to meeting the CAFE constraint.