Question

A 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 maximize the profit? Formulate this as a linear programming problem and solve it graphically

Answer 1

Let the no. of fans purchased by the dealer = x
and number of sewing machines purchased = y
then the L.P.P. is formulated as
Z = 22x + 18y to be maximised subject to constraints

Hence profit is maximum of Rs 392 when the dealer purchases 8 fans and 12 sewing machines.​