The Izza Steel Company of Tokyo has predicted delivery requirements of 3,000, 6,000, 5,000, and 2,000 tons of steel in the next four periods. Current workforce is at the 4,000 tons per period level. At the moment, there is 500 tons of steel in stock. At the end of the four periods, Izza would like its inventory position to be back at 500 tons. Regular time workforce has a variable cost of $100 per ton. Overtime can be hired in any period at a cost of $140 per ton. Regular time workforce size can be increased from one period to the next at a cost of $300 per ton of change in capacity. It can be decreased at a cost of $80 per ton. There is a charge of $5 per ton for inventory at the end of each period. Izza would like the regular time workforce to be at the 3,000-ton level at the end of the four periods. a) Formulate Izza's problem as a linear program.