Suppose dealer purchase x electronic sewing machines and y manually operated sewing machines. If Z denotes the total profit. Then according to question (Objective function) Z = 22x + 18 y
Also, x + y ≤ 20
360x + 240y ≤ 5760 ⇒ 9x + 6y ≤ 144
x ≥ 0, y ≥ 0.
We have to maximise Z subject to above constraint.
To solve graphically, at first we draw the graph of line corresponding to given inequations and shade the feasible region OABC.
The corner points of the feasible region OABC are O(0, 0), A(16, 0), B(8, 12) and C(0, 20).
Now the value of objective function Z at corner points are obtained in table as
Corner points |
Z = 22x + 18y |
O(0, 0) |
Z = 0 |
A(16, 0) |
Z = 22 x 16 + 18 x 0 = 352 |
B(8, 12) |
Z = 22 x 8 + 18 x 12 = 392 maximum |
C(0, 20) |
Z = 22 x 0 + 18 x 20 = 360 |
From table, it is obvious that Z is maximum when x = 8 and y = 12.
Hence, dealer should purchase 8 electronic sewing machines and 12 manually operated sewing machines to obtain the maximum profit ` 392 under given condition.