12. A company wants to plan production and inventory levels for its new product for the next 4 months so as to minimize the inventory holding and production costs. Demand is anticipated to be 130, 160, 270, and 150, respectively. The product is manufactured at the cost of $32 per unit. The cost of carrying one unit of inven- tory at the end of the month is $4. The inventory level at the beginning of the first month is 10 units and inventory required at the end is at least 20 units. Other information is given below: MONTH PRODUCTION CAPACITY 160 200 AWNI 210 160 a. Formulate a linear program, clearly defining all variables used, to determine the production and inventory in each period that minimizes the total cost. b. Use Solver to find the optimal solution to the linear program from part a