Question

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 using a subcontractor. The demand and projected capacities for three production options are in the following table:

	Month 1	Month 2	Month 3
demand (units)	25000	35000	45000
regular capacity	35000	30000	20000
overtime capacity	5000	5000	5000
subcontractor capacity	7500	2500	3500

The company can produce chairs at a cost of $50/unit in regular time and $70/unit using overtime. The subcontractor charges $90/unit to produce chairs. Placing chairs in storage for future use costs the company $20/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 problem into a linear program.
(d) Find the minimum cost to meet the demand requirements. What will be the cost to produce the chairs?

Answer 1

Ans. D. The Cost to produce the total # of Chairs is :

Demand for all the 3 months together is 25,000 +35,000+45,000=105,000 chairs.

Regular capacity is   : 35,000 +30,000+20,000= 85,000 chairs

The difference is 20,000 Chairs required to be made-up for demand

15,000 chairs are made up by Overtime capacity & 5,000 chairs are made by Subcontract

Cost to produce 35,000 chairs in the 1month = 35,000*$50=$1,750,000

Storage cost for future use=$20/unit/month =10,000*$20= $ 200,000

Overtime capacity to make 15,000*$70= $1,050,000

By Subcontract 5000*$90+ $ 450,000

Total Cost to produce the chairs        $ 3,450,000