A company manufactures two types of printed circuits. The requirements of transistors, resistors and capacitor for each type of printed circuits along with other data are given in table.

Circuit

Stock available (units)

A

B

Transistor

15

10

180

Resistor

10

20

200

Capacitor

15

20

210

Profit

Rs.5

Rs.8


How many circuits of each type should the company produce from the stock to earn maximum profit.
[Ans. Max Z = 82, 2 units of type A circuit and 9 units of type B circuit]
2. A company making cool drinks has 2 bottling plants located at towns T1 and T2. Each plant produces 3 drinks A, B and C and their production capacity per day is given in the table.
Cool drinks

Plant at

T1

T2

A

6000

2000

B

1000

2500

C

3000

3000

The marketing department of the company forecasts a demand of 80000 bottles of A, 22000 bottles of B and 40000 bottles of C during the month of June. The operating cost per day of plants at T1 and T2 are Rs. 6000 and Rs. 4000 respectively. Find graphically the number of days for which each plants must be run in June so as to minimize the operating cost while meeting the market demand.
[Ans. Min Z = Rs. 88000, 12 days for the plant T1 and 4 days for plant T2]
Solve the following LPP by graphical method
 Max Z = 3x_{1} + 4x_{2}
Subject to
x_{1 } x_{2 }≤ 1
x_{1}+ x_{2 }≤ 0
x_{1 }≥ 0 , x_{2 }≥ 0
[Ans. The problem has no solution]
 Max Z = 3x_{1} + 2x_{2}
Subject to
2x_{1 }+ 3x_{2 }≤ 9
x_{1} 5x_{2 }≥ 20
x_{1 }≥ 0 , x_{2 }≥ 0
[Ans. The problem has unbounded solution]
 Max Z = 45x_{1} + 80x_{2}
Subject to
5x_{1 }+ 20x_{2 }≤ 400
10x_{1}+ 15x_{2 }≤ 450
x_{1 }≥ 0 , x_{2 }≥ 0
[Ans. Max Z = 2200, x_{1} = 24, x_{2 }= 14]