A manufacturer produces two products, A and B, and is trying to work out his production schedule for the next two months. He currently has on hand 1,000 units of A and 800 units of B and estimates sales over the period as shown in the following table: Estimated Sales, Units/Months A B 1 2,000 3,000 2 3,000 4,000 Regular Shift Production Cost, $10 $6 $/Unit If the production facilities were devoted entirely to producing product A, they could turn out a maximum of 4,000 units/month on regular shift operation and up to 1,000 units/month additional on overtime operation. Similarly, if only product B was produced, regular shift capacity would be 6,000 units/month with 2,000 units/months additional available from overtime operation. The production facilities can be devoted to any proportions of products A and B - e.g., 1,000 units of A (= 1/4 capacity) plus 4,500 units of B (= 3/4 capacity) would just use the total regular shift capacity for a month. Overtime production of product A costs $5/unit more than regular shift production, while for product B the added cost is $3/unit. Management would like to end the two-month period with at least an inventory of 500 units of product A and 1,500 units of product B. It costs $3 to store one unit of Product A for a month and $2 to store one unit of product B for a month. a. Formulate algebraically the linear programming model for this production scheduling problem. Define the decision variables, objective function, and constraints