A company that produces chairs has obtained a demand forecast for the next three months. To meet the demand, the company can produce chairs using regular production time, overtime, and through a subcontractor. The demand and projected capacities for three production options are in the following table:

month 1 2 3

demand (units) 2,500 3,000 6,500

regular capacity 3,500 3,000 4,000

overtime capacity 500 0 750

subcontractor capacity 7,500 2,500 3,500

The company can produce chairs at a cost of $50/unit in regular time and $70/unit using overtime. The subcontractor charges $110/unit to produce chairs. An existing contract forces the company to order at least 100 chairs per month from the subcontractor. Placing chairs in storage for future use costs the company $40/unit per month.

(a) Construct a network representation of the production problem.

(b) Is the company capable of meeting the demand requirements?

(c) Convert the network representation into a linear program.

(d) Find the minimum cost to meet the demand requirements. What will be the cost to produce the chairs?