The Martinez Model Car Company produces four different radio$-$controlled model cars based on exotic production models: Ferrari, BMW$,$ Lotus, and Tesla. Each model requires production in five departments: molding, sanding, polishing, painting, and finishing. The number of minutes required for each product in each department, the selling price per unit, and the minutes available in each department each day are provided. Only whole numbers of cars are counted. a$.$ Martinez Model Cars Minutes$/$Unit Ferrari BMW Lotus Tesla Minutes Available Mold $5\mathrm{.}003\mathrm{.}501\mathrm{.}003\mathrm{.}00600$ Sand $4\mathrm{.}003\mathrm{.}202\mathrm{.}003\mathrm{.}65600$ Polish $3\mathrm{.}502\mathrm{.}003\mathrm{.}001\mathrm{.}00480$ Paint $3\mathrm{.}753\mathrm{.}251\mathrm{.}752\mathrm{.}00480$ Finsih $4\mathrm{.}001\mathrm{.}002\mathrm{.}003\mathrm{.}00480$ Price $$350\mathrm{.}00$ $$330\mathrm{.}00$ $$270\mathrm{.}00$ $$255\mathrm{.}00$ How many of each type of car should be produced to maximize profit? If marketing requires that at least $40$ units of each be produced each day, what is the optimal production plan and profit? Before you solve this, how would you expect the profit to compare with your answer to part a$?$What happens if marketing requires that at least $50$ units of each be produced each day?