Question $1$: Formulate a Linear Program $(30$ Points$)$ Patagonia, Inc. is working on developing a new workwear line of clothes, and much of the work centers on developing new fabrics. A new outerwear fabric is requested from the product designers, which could be made with a combination of different fibers, including cotton, hemp, polyester, wool, and spandex. Each of these component fibers has a warmth, stretch, and strength rating per pound $($seen in the table below$),$ and the final blend of fibers must meet minimum requirements in each of these dimensions. There are several additional requirements. First, at least $55\%$ of the final blend needs to be some combination of cotton and hemp. Spandex should not be more than $8\%$ of the final blend. Finally, the total weight of the blend should not exceed $1\mathrm{.}5$ Ibs. Patagonia would like to find the ideal blend of fibers to meet these specifications in the most cost$-$effective way. Formulate this problem as a linear program, in the textbox to the right.