Question

a shoe manufacturer produces midtoop and high top athletic shoes. cutting machines cut the fabric for shoes. stitching machine stitch the fabric. the cutting machines run 4 hours per day, and the stitching machines run 5 hours per day. a midtop shoe takes 3 minutes to cut and 2 minutes to stitch the profit is $13 on a midtop shoe and $16 on a hightop shoe. write the constraints

Answer 1

Let the manufacturer makes $x$ pairs of mid-top athletic shoes and $y$ pairs of high-top athletic shoes per day.

$x\geq0, y\geq0$

A mid-top shoe takes 1 minute to cut.

A high-top shoe takes 3 minutes to cut.

The cutting machines run 4 hours per day.

$$x+3y\leq4(60)$$

A mid-top shoe takes 2 minutes to stitch.

A high-top shoe takes 2 minutes to stitch.

The stitching machines run 5 hours per day.

$$2x+2y\leq5(60)$$

Write the constraints

$$\begin{matrix} x+3y\leq180 \\ x+y\leq150 \\ x\geq0 , y\geq0 \end{matrix}$$