You have just been promoted to the position of production manager of ActiveWear, a clothing company specializing in the production of ski jackets. ActiveWear's most successful product to date is the Signature WindCrusher jacket, and you are now in charge of planning its production for the upcoming ski season. The WindCrusher comes in three sizes, small (S), medium (M) and large (L), and its production is based primarily on three materials, hydrophobic fabric, weather insulation material, and waterproof zipper. For each of the three sizes, the material requirements for the production of one jacket are given below:

• Small: 1 square yard fabric, 2 square yards insulation, 0.5 meters zipper
• Medium: 3 square yards fabric, 3 square yards insulation, 0.65 meters zipper
• Large: 4 square yards fabric, 5 square yards insulation, 0.7 meters zipper

Although there is ample demand for the WindCrusher jacket, there is limited availability of materials. In particular, there are only 1500 square yards of fabric, 2000 square yards of insulation, and 800 meters of zipper. The unit profit contributions for small, medium and large jackets are $40, $65 and $85 respectively.

Question 1

2 pts

[Problem 1, Question 1] Using the information given above, write down a linear program to identify the production of WindCrusher jackets that maximizes the total profit contribution, using XS to denote the production quantity of small jackets, XM to denote the production quantity of medium jackets, and XL to denote the production quantity of large jackets.