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Question:

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

Solution:

Let x and y be electronic and manually operated sewing machines purchased respectively.
Therefore, LPP is maximize P = 22x + 18y
Subjected to 360x + 240y ≤ 5760 or, 3x + 2y ≤ 48
x + y ≤ 20
x ≥ 0, y ≥ 0
For correct graph vertices of feasible region are A(0,20), B(8,12), C(16,0) and O(0,0)
P(A) = 360, P(B) = 392, P(C) = 352
3x + 2y = 48 ----(1)
x + y = 20 ----(2)
Solving equation (1) and (2), we get x = 8, y = 12
Therefore for maximum P, electronic machines = 8. Manual machines = 12.