You are a member of the financial planning office in a large corporation. You have been asked by the CFO (Chief Financial Officer) to develop a production plan for a current line of printers. Since this product is just one in a large product line, the CFO has requested that this particular product have a production schedule that keeps the average cost as low as possible (despite the fact that the item is a popular item and all units that can be manufactured can be sold). The last five years of data suggest that the daily cost function for these printers can be approximated by the function: C(x) = .000195*x^3- 1.14*x^2+50*x+2560, where C(x) is in dollars and x is the number of printers produced per day. Your task is to provide a recommended production daily schedule that will keep the average- cost-per- item as low as possible. The corporation prepared to manufacture from 90 to 900 units in a day. (Remark: An analysis of this problem will help us understand the relationship between costs, marginal costs, average costs, and marginal average costs.) 1. A range has been put in column A. Put the cost function in column B (you can copy it from this sheet and paste it on the next sheet.) Find (by hand) the marginal cost function. Find the cost and marginal cost for weekly production levels over your X-range. Graph (on separate graphs, because they have very different y-values, labeling each appropriately, of course) the cost and marginal cost functions. 2. Find (and put in column C) and graph (and label) the average-cost function AC(x) for your x-range. (Hint: average cost = total cost / #units.) 3. Find (and put in column D) and graph (and label) the marginal-average-cost function MAC(x). 4. Use your marginal average cost function (and the Solver, GoalSeek, or other methods) to find the Iproduction level which will minimize average cost. 5. Using the information above, write a short paragraph describing your recommendation to the CFO on the appropriate daily production schedule that will keep the average cost figures low. Be sure to justify your answer using your computations. This will count for 34% of your grade on your lab, so please make it more than a sentence! (Use Landscape View for your pages and it should print out without too much playing around.) Cix MC(x) Chart (24pts MAC(x) AC(x) Graph C(x) here (8pts) 90 180 270 360 450 540 630 720 810 900 Graph AC(x) here. (8pts) Graph MC(x) here. (Spts) Names: Graph MAC(x) here. (pts) Write your recommendation to the CFO here. (34pts) You are a member of the financial planning office in a large corporation. You have been asked by the CFO (Chief Financial Officer) to develop a production plan for a current line of printers. Since this product is just one in a large product line, the CFO has requested that this particular product have a production schedule that keeps the average cost as low as possible (despite the fact that the item is a popular item and all units that can be manufactured can be sold). The last five years of data suggest that the daily cost function for these printers can be approximated by the function: C(x) = .000195*x^3- 1.14*x^2+50*x+2560, where C(x) is in dollars and x is the number of printers produced per day. Your task is to provide a recommended production daily schedule that will keep the average- cost-per- item as low as possible. The corporation prepared to manufacture from 90 to 900 units in a day. (Remark: An analysis of this problem will help us understand the relationship between costs, marginal costs, average costs, and marginal average costs.) 1. A range has been put in column A. Put the cost function in column B (you can copy it from this sheet and paste it on the next sheet.) Find (by hand) the marginal cost function. Find the cost and marginal cost for weekly production levels over your X-range. Graph (on separate graphs, because they have very different y-values, labeling each appropriately, of course) the cost and marginal cost functions. 2. Find (and put in column C) and graph (and label) the average-cost function AC(x) for your x-range. (Hint: average cost = total cost / #units.) 3. Find (and put in column D) and graph (and label) the marginal-average-cost function MAC(x). 4. Use your marginal average cost function (and the Solver, GoalSeek, or other methods) to find the Iproduction level which will minimize average cost. 5. Using the information above, write a short paragraph describing your recommendation to the CFO on the appropriate daily production schedule that will keep the average cost figures low. Be sure to justify your answer using your computations. This will count for 34% of your grade on your lab, so please make it more than a sentence! (Use Landscape View for your pages and it should print out without too much playing around.) Cix MC(x) Chart (24pts MAC(x) AC(x) Graph C(x) here (8pts) 90 180 270 360 450 540 630 720 810 900 Graph AC(x) here. (8pts) Graph MC(x) here. (Spts) Names: Graph MAC(x) here. (pts) Write your recommendation to the CFO here. (34pts)