3. The Kew Toy Company’s production manager wonders whether to produce at a level production rate or a rate that matches sales each quarter. His analysis of company operations yields the following information:

Beginning employment level ???? 10 employees.

Beginning inventory ???? 0 Hiring cost ???? $10 per employee.

Firing cost ???? $5 per employee.

Production per employee ???? 10 units per quarter.

Inventory carrying costs ???? $1 per unit per quarter (on ending inventory).

Target inventory at the end of the fourth quarter ???? 0.

Target employment level at the end of the fourth quarter equals the planned.

Employment level specified by the plan under consideration.

Sales Quarter Forecast (Units)

1 50 2 80 3 120 4 150

a. Which of the two policies would result in the lowest annual cost?

b. What’s the total annual cost of the policy adopted in part 1?

c. What production rate should he use each quarter?

d. Formulate this problem so it can be solved using linear programming.