2. Answer EITHER (a) OR (b) below. If you choose to work on more than one, please indicate which one you want me to grade. You will not get extra points for doing both problems. [8 points] a. Mrs. Louchart's Hand Sanitizer Supply store sells 32 cases of Deluxe Sanitizer per month, at a price of $2800 each. Market research indicates that they could sell one additional case for each $40 reduction in price. Let x be the number of $40 reductions in price. Write a function that gives the revenue as a function of x, then use calculus to determine the price that will result in maximum revenue for the store. Round answer to 2 decimal places, if necessary. Function Case price that will maximize revenue_ b. Suppose we need to make a rectangular pen, divided down the middle into two smaller areas. The pen will be built against an existing wall, so the left side does not need any fencing. (See figure below.) The pen must have a total area of 1200 m. Let x be the horizontal width of the pen. The fencing needed for the three horizontal sides costs $20/m, and the fencing needed for the vertical side costs $40/m. Write a function that gives the total cost for the fencing as a function of x, then use calculus to determine the width of the pen that will minimize the total cost. Round answer to 2 decimal places, if necessary. Function giving cost of fencing Width of pen needed to minimize cost 2. Answer EITHER (a) OR (b) below. If you choose to work on more than one, please indicate which one you want me to grade. You will not get extra points for doing both problems. [8 points] a. Mrs. Louchart's Hand Sanitizer Supply store sells 32 cases of Deluxe Sanitizer per month, at a price of $2800 each. Market research indicates that they could sell one additional case for each $40 reduction in price. Let x be the number of $40 reductions in price. Write a function that gives the revenue as a function of x, then use calculus to determine the price that will result in maximum revenue for the store. Round answer to 2 decimal places, if necessary. Function Case price that will maximize revenue_ b. Suppose we need to make a rectangular pen, divided down the middle into two smaller areas. The pen will be built against an existing wall, so the left side does not need any fencing. (See figure below.) The pen must have a total area of 1200 m. Let x be the horizontal width of the pen. The fencing needed for the three horizontal sides costs $20/m, and the fencing needed for the vertical side costs $40/m. Write a function that gives the total cost for the fencing as a function of x, then use calculus to determine the width of the pen that will minimize the total cost. Round answer to 2 decimal places, if necessary. Function giving cost of fencing Width of pen needed to minimize cost