# How do I convert this to a linear programming problem?

It takes a tailoring 2 hours of cutting and 4 hours of sewing to make a knit suit. To make a worsted suit, it takes 4 hours of cutting and 2 hours of sewing. At most 20 hours per day are available for cutting and at most 16 hours per day are available for sewing. The profit on a knit suit is Php340 and on worsted suit is Php310. How many of each kind of suit should be made to maximize profit? What is the maximum profit?

You are told "It takes a tailoring 2 hours of cutting and 4 hours of sewing to make a knit suit." so to make x knit suits, it will take 2x hours of cutting and 4x hours of sewing. You are told "To make a worsted suit, it takes 4 hours of cutting and 2 hours of sewing" so to make y worsted suits, it will take 4y hours of cutting and 2 hours of sewing. To make x knit suits and y worsted suits will take 2x+ 4y hours of cutting and 4x+ 2y hours of sewing. You are told "At most 20 hours per day are available for cutting" so $2x+ 4y\le 20$. You are told "at most 16 hours per day are available for sewing." so $4x+ 2y\le 16$. Finally, you are told that "The profit on a knit suit is Php340 and on worsted suit is Php310." so with x knit suits and y worsted suits the profit will be 340x+ 310y.
The problem is to maximize 340x+ 310y subject to the constraints $2x+ 4y\le 20$ and $4x+ 2y\le 16$. (And, of course, $x\ge 0$, $y\ge 0$.)