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.

Layoff 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.

a. Develop level production and chase production plans, given the data provided.

b. Which plan has the lowest total annual cost?

c. What production rate should be used each quarter in the low cost plan?

d. Formulate this problem so it can be solved using LP.

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Quarter 1 2 234 Planned Sales (Units) 50 80 120 150