# A manufacturer wishes to plan the production of two items A and B for the months of March, April,…

A manufacturer wishes to plan the production of two items A and B for the months of March, April, May, and June. The demands that must be met are given below:

Suppose that the inventory of A and B at the end of February is 100 and 150, respectively. Further suppose that at least 150 units of item B must be available at the end of June. The inventory holding costs of items A and B during any month are given by \$ 1.20 and \$ 1.00 times the inventory of the item at the end of the month. Furthermore, because of space limitation, the sum of items A and B in stock cannot exceed 250 during any month. Finally, the maximum number of items A and B that can be produced during any given month is 550 and 650, respectively.

a. Formulate the production problem as a linear program. The objective is to minimize the total inventory cost (the production cost is assumed constant).

b. Find an optimal production/inventory pattern.

c. Management is considering installing a new manufacturing system for item B at the end of April. This would raise the maximum items that can be produced per month from 650 to 700, and meanwhile would reduce the unit manufacturing cost from \$8.00 to \$6.50. Assess the benefits of this system in reducing the total manufacturing costs plus inventory costs. If you were a member of the management team, discuss how you would assess whether the new system is costeffective.

d. Suppose that management decided to introduce the new system. Market research indicated that item B can be backlogged without serious dissatisfaction of customers. It was the management&#39;s assessment that each unit of unsatisfied demand during any month must be charged an additional \$1.00. Formulate the production/inventory problem and find an optimal solution by the simplex method.

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