Consider the problem of scheduling the weekly production of a certain item for the next 4 weeks. The production cost of the item is $10 for the first 2 weeks, and $15 for the last 2 weeks. The weekly demands are 300, 700, 900, and 800 units, which must be met. The plant can produce a maximum of 700 units each week. In addition the company can employ overtime during the second and third weeks. This increases the weekly production by an additional 200 units, but the cost of production increases by $5 per item. Excess production can be stored at a cost of $3 an item per week. How should the production be scheduled so as to minimize the total costs? Formulate this as a linear programming problem.