Problem 4. (70 points) Bearcats Aluminum Co. has received order for aluminum for each of the next four months, as given in the table below. Bearcats can meet these demands by producing the aluminum, by drawing from inventory, or by any combination thereof. Because of the inflationary production costs given in the table, Bearcats can produce more aluminum than needed in each month, up to a maximum of 4000 tons. All production takes place at the beginning of the month, after which the demand is met and the remaining steel is stored in inventory, at a cost of $120 per ton for one month. Also, each ton of increased or decreased production from one month to the next incurs an additional change-inproduction cost of $50, except for the first month, which is exempt. The inventory at the beginning of the first month is 1000 tons, and there must be at least 1500 tons of inventory at the end of the fourth month. a. (30 points) Formulate an optimization problem in mathematic form that can be used to find the optimal four-month production plan that minimizes the total costs. b. (40 points) Solve the optimization model you formulated in part (a) on a spreadsheet