Problem $3(30$ points$)$

XYZ Company has just entered the market with a new pocket computer. Although the company is starting with modest

sales, it expects to grow before leveling off at $6000$ units per month as shown in the following table

The company currently has $50$ workers each of whom can assemble $100$ computers per month. It costs AED $5000$ to hire

a new worker and AED $10000$ to fire an employee. Each employee earn AED $3000$ per month. It costs AED $10$ to

store one unit in inventory or one month. There are $400$ units on hand at the beginning of month $1.$ Calculate the

cost of each of the following plan.

a$-$ Varying the workforce $(15$ points$)$

b$-$ Keep the workforce constant $(15$ points$)$