Mountain outfitters makes hand-knit wool products from the finest yak-blended wool in the world. Their Mountain line consists of a sweater, a hat and a pair of mittens, all using the same pattern, which is custom designed for each writers National Cup competition. The forecast demand and the profit (for contribution) margins for each product are given in the table below.

Mountain Outfitters has limited supply of the three Indie dyed colors used to make their wool products. They can acquire 720,000 yards of gray, and 410,000 yards of red. This years National Cup patterns require various amounts of these three colors for each product as given in the table below (all amounts are measured in yards).

Because many customers like to buy a hat with a pair of mittens, Mountain Outfitters wants to ensure that the number of mitten pairs is at least of the number of hats produced. To ensure balanced production of all products, the number of sweaters should be at most of the number of hats and mitten pairs combined. Based on this information, how many sweaters, hats and pairs of mittens should they produce?

Write down your formulation, solve it in excel, and report your optimal production quantities and optimal value.

1b) (9 points)

Suppose Mountain Outfitters insists that, if they make a product, they want to make at least 1000. What changes must you make to your formulation in part (a) to do this? (Note: you need only specify what changes or additions are needed to the objective function, the constraints and/or the decision variables in your original model. You may write out the new formulation if you wish).

Solve your new model in Excel and report your new optimal production quantities and optimal value. You may require integer production quantities (sweater, hats, mittens) if you wish, but it is not strictly required.

Hint: consider three additional variables to model whether at least 1000 of each product will be produced.

\begin{tabular}{|l|l|l|l|} \hline & Sweater & Hats & Mittens \\ \hline Forecasted demand & 2300 & 2900 & 1800 \\ \hline Profit Margin & $1200 & $265 & $300 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline & Sweater & Hats & Mittens \\ \hline Ecru & 400 yards & 100 yards & 150 yards \\ \hline Gray & 600 yards & 300 yards & 300 yards \\ \hline Red & 300 yards & 0 yards & 100 yards \\ \hline \end{tabular}