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Refer to Example 1. The president of the firm has decided to shut down the plant for vacation and installation of new equipment in period 4. After installation, the cost per unit will remain the same, but the output rate for regular time will be 450. Regular output is the same as in Example 1 for periods 1, 2, and 3; 0 for period 4; and 450 for each of the remaining periods. Note, though, that the forecast of 400 units in period 4 must be dealt with. Prepare the aggregate plan, and compute its total cost. 2. Refer to Example 1. Suppose that the regular output rate will drop to 290 units per period due to an expected change in production requirements. Costs will not change. Prepare an aggregate plan and compute its total cost for each of these alternatives: a. Use overtime at a fixed rate of 20 units per period as needed. Plan for an ending inventory of zero for period 6. Backlogs cannot exceed 90 units per period. b. Use subcontracting at a maximum rate of 50 units per period; the usage need not be the same in every period. Have an ending inventory of zero in the last period. Again backlogs cannot exceed 90 units in any period. Compare these two plans. 3. Refer to Example 2. Suppose you can use a combination of overtime and subcontracting, but you cannot use subcontracting in more than two periods. Up to 50 units of subcontracting and either 0 or 40 units of overtime are allowed per period. Subcontracting is $6 per unit, and overtime is $3 per unit. (Hint: Use subcontracting only when overtime units are not sufficient to decrease backlogs to 80 units or less.) Plan for an ending inventory balance of 0 for period 6. Prepare a plan that will minimize total cost