Type the linear program, optimal solution, and objective function value in a word document.

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#$1)$ A small backpack manufacturer carriers four different models of backpacks, made of canvas, plastic, nylon, and leather. The bookstore, which will sell the backpacks exclusively, 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 week. One worker can work on either canvas or plastic, can complete a backpack in $1\mathrm{.}5$ hours, and will charge $$7\mathrm{.}25$ per hour to do the work. This worker can work a maximum of $90$ hours during the week. Another worker can sew backpacks made of nylon fabric. He can complete a bag in $1\mathrm{.}7$ hours, will charge $$8\mathrm{.}25$ 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 can complete a backpack in $1\mathrm{.}9$ hours, will charge $$9\mathrm{.}25$ per hour to work, and can work $80$ hours during the next week. The following table provides additional information about each backpack. What is the best combination of backpacks to provide the store to maximize profit?

$\backslash$table$[[$Model$,$Material Required,Material Available,Cost$/$ Square Yard$],[$Canvas$,2\mathrm{.}15,200,$$$4\mathrm{.}25$