$1.$ 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 forlight trucks is $17.2.$ Using Excel Solver or LINGO, find the price for each car so that the total profitcontribution is maximized. $3.$ Given the prices determined in Question $2,$ calculate the number of passenger carssold and the number of light trucks sold. $4.$ Duplicate the spreadsheet in Figure $12\mathrm{.}17.$ Your spreadsheet should have formulas in cells D$3$:D$5$ and B$7$ and be able to calculate the harmonic $($CAFE$)$ average forany MPG rating and any number of vehicles in each category. $5.$ Again, assuming that passenger cars get $30$ MPG and light trucks get $20$ MPG$,$calculate the CAFE average for the fleet size from Question $3\mathrm{.}6.$ 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 $25$ MPG and re$-$solve the modelto get the maximum total profit contribution subject to meeting the CAFE constraint.