Question: Write the Linear Programming formulations for the following problem
Western Swiss Machine shop makes deluxe and regular skis on a weekly schedule for the area skiing enthusiasts. They have a contract with Apple Hill to supply 18 regular pairs of skis per week. They also sell both regular and deluxe skis to local sporting goods stores. A deluxe pair of skis requires 40 minutes for roughing and 20 minutes for finishing, while a regular pair of skis requires 20 minutes for roughing and 26 minutes for finishing. Only 1000 minutes for roughing and 800 minutes for finishing are available each week. Regular skis contribute $30 to profit per pair while deluxe skis contribute $40 per pair.
Formulate the problem as a LP problem that will determine how many pairs of each type of ski Western Swiss should produce weekly in order to meet the contract requirement and maximize profit.