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

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 $1.00 and $0.80 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 month is 500 and 650 respectively.

a.)  Formulate the production problem as a linear program to minimize the total cost of inventory.

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 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 cost-effective.

d.)  Suppose management decided to introduce the new system. Market research indicated that the item B can be backlogged without serious dissatisfaction of customers. It was the management’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 using Excel Solver, explain the answer, explain shadow prices.

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