A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 workers (male and female) and 17 units capital; which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at Rs. 100 and Rs. 120 per unit respectively, how should he use his resources to maximise the total revenue? Form the LPP and solve graphically.
Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?
A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 workers (male and female) and 17 units capital; which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at Rs. 100 and Rs. 120 per unit respectively, how should he use his resources to maximise the total revenue? Form the LPP and solve graphically.
Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?
The correct option is B 1260
Let the number of goods of type A and B produced be respectively x and y.
To maximize, Z=(100x+120y)
Subject to the constraints:
2x+3y≤30 ---- (1)
3x+y≤17---- (2) where x,y≤0.
Take the testing points as (0,0) for (1) we have: 2(0)+3(0)≤30⇒0≤30, which is true.
Take the testing points as (0,0) for (2) we have: 3(0)+(0)≤17⇒0≤17, which is true.
The shaded region OACBO as shown in the given figure is the feasible region, which is bounded.
The coordinates of the corner points of the feasible region are A(173,0),E(3,8),C(0,10)andO(0,0).
So, Value of Z at A(173,0)=17003
Value of Z at B(0,10)=1200
Value of Z at C(3,8)=1260
Value of Z at O(0,0)=0
Pts. Coordinate Zmax=100x+120y O (0,0) Z=0 A (173,0) Z=17003 E (3,8) Z=300+960=1260 C (0,10) Z=1200
The maximum value of Z is Rs.1260 which occurs at x=3 and y=8.
Thus the factory must produce 3 units and 8 units of the goods of type A and B respectively. The maximum obtained profit earned by the factory by producing these items is Rs.1260.
Yes, we agree with the view of manufacturer that men and women workers are equally efficient and so should be paid at the same rate.
Let the number of goods of type A and B produced be respectively x and y.
To maximize, Z=(100x+120y)
Subject to the constraints:
2x+3y≤30 ---- (1)
3x+y≤17---- (2) where x,y≤0.
Take the testing points as (0,0) for (1) we have: 2(0)+3(0)≤30⇒0≤30, which is true.
Take the testing points as (0,0) for (2) we have: 3(0)+(0)≤17⇒0≤17, which is true.
The shaded region OACBO as shown in the given figure is the feasible region, which is bounded.
The coordinates of the corner points of the feasible region are A(173,0),E(3,8),C(0,10)andO(0,0).
So, Value of Z at A(173,0)=17003
Value of Z at B(0,10)=1200
Value of Z at C(3,8)=1260
Value of Z at O(0,0)=0
| Pts. | Coordinate | Zmax=100x+120y |
| O | (0,0) | Z=0 |
| A | (173,0) | Z=17003 |
| E | (3,8) | Z=300+960=1260 |
| C | (0,10) | Z=1200 |
The maximum value of Z is Rs.1260 which occurs at x=3 and y=8.
Thus the factory must produce 3 units and 8 units of the goods of type A and B respectively. The maximum obtained profit earned by the factory by producing these items is Rs.1260.
Yes, we agree with the view of manufacturer that men and women workers are equally efficient and so should be paid at the same rate.
