A dealer in rural area wishes to purchase a number of sewing machines. He has only
₹ 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him ₹ 360 and a manually operated sewing machine ₹ 240. He can sell an electronic sewing machine at a profit of ₹ 22 and a manually operated sewing machine at a profit of ₹ 18.Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit? Make it as a LPP and solve it graphically.

Let x and y be electronic and manually operated sewing machines purchased respectively.

Given that, x+y≤ 20 and 360x+240y≤ 5760 ⇒ 3x+2y≤ 48

Total profit, Z = 22x+18y

We have the following mathematical model for the given problem

Maximize, Z = 22x+18y

Subject to

3x+2y≤ 48

x+y≤ 20

x≥ 0, y≥ 0

Now, plot the lines corresponding to given inequalities on graph and shade the feasible region.

The feasible region OABC determined by the linear inequalities shown in figure. Note that the feasible region is bounded.

The corner points of the feasible region OABC are 0(0,0) , A(16,0) ,B(8,12) and C(0,20).

Let us evaluate the objective function Z at each corner point.

We find that maximum value of Z is 392 at B(8,12).Hence, the dealer should purchase 8 electronic sewing machines and 12 manually operated sewing machines to obtain the maximum profit Rs. 392 under given condition.