A manufacturer has employed 5 skilled men and 10 semi-skilled men and makes two models A and B of an article. The making of one item of model A requires 2 hours of work by a skilled man and 2 hours work by a semi-skilled man. One item of model B requires 1 hour by a skilled man and 3 hours by a semi-skilled man. No man is expected to work more than 8 hours per day. The manufacturer’s profit on an item of model A is Rs. 15 and on an item of model B is Rs 10. How many items of each model should be made per day in order to maximize daily profit? Formulate the above LPP and solve it graphically and find the maximum profit.
Let be the number of items of model A and be the number of items of model B.
Let be the required profit
Subject to constraints
Maximize
Changing the above inequalities to equations
x | 0 | 20 |
y | 40 | 0 |
x | 0 | 40 |
y | 80/3 | 0 |
Now, plotting these points on the graph
In graph: the shaded region is the required feasible region.
Vertices | maximum |
O(0,0) | |
A(20,0) | |
B(10,20) | |
C(0, ) |
Maximum profit is obtained when the manufacturer produces 10 items of model A & 20 items of model B and the maximum profit is: 350