A dealer wishes to purchase a number of fans and sewing machines. He has only $\pm 5760$ to invest and space and $\pm 18$ on a sewing machine. Assuming that he can sell all the items he can buy, how should he invest the money in order to maximize the profit?

Home » A dealer wishes to purchase a number of fans and sewing machines. He has only to invest and space and on a sewing machine. Assuming that he can sell all the items he can buy, how should he invest the money in order to maximize the profit?

A dealer wishes to purchase a number of fans and sewing machines. He has only $\pm 5760$ to invest and space and $\pm 18$ on a sewing machine. Assuming that he can sell all the items he can buy, how should he invest the money in order to maximize the profit?

Let the number of fans bought be $x$ and sewing machines bought be $y$ .
$\therefore$ According to the question,
$360 x+240 y \leq 5760, x+y \leq 20, x \geq 0, y \geq 0$
Maximize $Z=22 x+18 y$
The feasible region determined by $360 x+240 y \leq 5760, x+y \leq 20, x \geq 0, y \geq 0$ is given by