Dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760 to invest and has a space for at most 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he can sell a fan at a profit of Rs. 22 and a 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 minimize the profit? Formulate This as a linear programming problem and solve it graphically.
Verified Answer
Let dealer purchases x fans and y sewing machines,
Then LPP is
To maximize Z = 22x + 18y
Subject to constraints,
x3 0, y3 0, x + y. f 20, 360x + 24y f 5760
⇒ 3x + 2y ≤ 48
On plotting the above inequations on the graph, we get shaded portion as the feasible solution.
Possible points for maximum Z are A(16, 0), B(8,12), and C(0, 20).
Z is maximum at B(8,12) i.e., x = 8 , y = 12.
Hence 8 fans and 12 sewing machines must be purchased for a maximum profit of Rs. 392.