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
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.
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