make an LP model based of off these direction:

CASE $1$: Kootenay Straw Broom Company

The Kootenay Straw Broom Company, located in British Co$-$

Kootenay is a family$-$run business, It considers the daily cost

lumbia, Canada, is a small, family$-$run business that hand$-$

of $$2300$ for its overhead and "family labor' of its $10$ members

makes two models of straw brooms, the Pioneer and the Her$-$

as sunk costs required for the business. Kootenay is ready to

itage models, which are sold in "country stores" throughout $-$

consider several options that could increase the daily profit:

Canada and the northwestern United States. Given its current production capacity and selling price, Kootenay is able to sell all the brooms it produces.

The Pioneer model is the company's basic model. It consists of a plain wooden handle, utilizes one pound of straw, and takes an average of $15$ minutes $(25$ hours$)$ to make.

Kootenay sells them for $$12\mathrm{.}75$ each. The Heritage model is the companys deluxe model. Although the same wooden handies are used, they are run through a decorative lathe and attached to a larger base consisting of $1\mathrm{.}5$ pounds of straw.

These two factors increase the production time of the Heritage broom to $24$ minutes $(\mathrm{.}40$ hours$),$ and Kootenay sells them for $$18$ each.

Kootenay receives daily deliveries of straw that is specially treated for their brooms from Tyler Farms. Tyler can supply Kootenay with up to $350$ pounds daily of the specially treated straw. This straw costs Kootenay S$1\mathrm{.}50$ per pound.

Kootenay purchases its handles from Adhor Mills, which manufactures the handles according to Kootenay's specifi$-$catient mohes onis one day dour ato one mayor truck

capable of hauling $30$ boxes of $10$ handles each $($or $300$ han$-$dies$).$ Adhor charges Kootenay$$$$7\mathrm{.}50$ per box of $10$ for manufacture and delivery of the handles.

Adhor also makes a major delivery of products to a town $45$ miles from Kootenay and has offered to swing by Kootenay with one additional box of $10$ handles. However, the added expense for making this detour means that Kootenay would have to pay Adhor $$25$ for this extra box of $10$ handles.

Kootenay averages $80$ production hours per day. Since

Seeking additional sources for treated straw

$2..$

Taking Adhor Mills up on its offer to deliver an extra box. of handles $($for $$25)$

$3.$ Adding a half$-$time worker $($four hours per day$)$ for $$50$per day

Prepare a report for the Kootenay Straw Broom Company that evaluates the option or set of options it should imple$-$ment. The report should:

$$Recommend an optimal production under current con$-$ditions.

$$Include a summary of the determination of unit profits of $$10\mathrm{.}50$ and $$15\mathrm{.}00,$ respectively, for the Pioneer and Broom models, showing that the cost of both treated straw and broom handles are included in these calcula$-$tions.

$$Show that after subtracting fixed costs, the business nets $$500$ per day.

$$Give a brief analysis of the sensitivity of the objective function coefficients.

$$Analyze the options using the correct interpretation of the shadow prices considering which costs are included and which costs are sunk. $($Remmer$.$ Do not call them shadow prices in the report.

$$Use the $100\%$ rule te evaluate whether more than one option should be implemented. $($Calculations$,$ if shown. should be placed in an appendix.$)$