$3-1$ A small backpack manufacturer carries four different

models of backpacks, made of canvas, plastic, nylon,

and leather. The bookstore, which will exclusively

sell the backpacks, expects to be able to sell between

$15$ and $40$ of each model. The store has agreed to pay

$$35\mathrm{.}50$ for each canvas backpack, $$39\mathrm{.}50$ for each

plastic backpack, $$42\mathrm{.}50$ for each nylon backpack,

and $$69\mathrm{.}50$ for each leather backpack that can be

delivered by the end of the following week.

One worker can work on either canvas or plastic,

can complete a backpack in $1\mathrm{.}5$ hours, and will charge

$$7\mathrm{.}00$ per hour to do the work. This worker can work a

maximum of $90$ hours during the next week. Another

worker can sew backpacks made of nylon fabric. He can

complete a bag in $1\mathrm{.}7$ hours, will charge $$8\mathrm{.}00$ per hour

to work, and can work $42\mathrm{.}5$ hours in the next week. A

third worker has the ability to sew leather. He each can

complete a book bag in $1\mathrm{.}9$ hours, will charge $$9\mathrm{.}00$ per

hour to work, and can work $80$ hours during the next

week. The following table provides additional informa$-$

tion about each backpack. What is the best combination

of backpacks to provide the store to maximize the profit?

HINTS:

$1)$ Profit Equation

$2)$ CONSTRAINTS $7$ lines

$3)$ MAX$-4$ lines

$4)$ MIN $4$ lines

$5)$ You must set your data table like the examples in the slides and textbook

$6)$ Your data needs to include LHS$,$ SIGN, and RHS