A toymaker manufactures two types of toys: A and B. To manufacture one unit of A, 1.5 kg
of plastic and 2.5 kg of wood are required. To manufacture product B, 2.5 kg of plastic and
1.5 kg of wood are required. In a month, 300 kg of plastic and 240 kg of wood are available.
Profit per unit for A is Rs. 50 and for B is Rs. 40.
1. Formulate as LPP.
Answer-
plastic wood
A 1.5 KG 2.5 KG
B 2.5 KG 1.5 KG
<= 300 kg <=240 kg
Subject to constraints
1.5x+2.5y<= 300
2.5x+1.5y<= 240
X<0
Y<0
Maximise- 50x+40y
A mining company is planning to extract rare-earth material for the next four months
(October, November, December, January) with monthly demands for the four months as 52,
72, 52, and 62 quintal. The company has a permanent work force of 100 employees. To meet
any additional demand in a given month, the company can hire temporary workers on a
monthly basis and can also fire them by the end of the month when their service is no more
required. The costs associated with hiring and firing one employee are 200 Rs. and 400 Rs.
respectively (overhead administrative costs). One permanent employee can extract 0.12
quintal of the material, on average, per month. Due to lack of experience, the temporary
hires can extract only 0.10 quintal per month. The carrying cost of one quintal of the
material for one month is 500 rs.
1. What is the objective function of the problem?
2. What are the decision variables involved in this problem?
3. Formulate the Linear programming problem.
4. Can we have hiring and firing happening in the same month?
