1. [15 points] An electric company makes motors for a variety of applications. Its two plants ship their production to three dealers. The production hours available in the plants for the second quarter vary because of downtime for scheduled maintenance on equipment: Plant April May June A 400 360 360 B 425 350 375 Plant A requires 20 hours to produce a motor. Plant B requires 25. Because B is older and less efficient, production costs are $100 more per motor in B than in A. Shipping costs from the plants to the dealers and orders for the quarter are show below Monthly Shipping orders costs from Dealer April May June A B 1 12 9 11 45 60 2 10 12 8 50 70 3 8 11 12 75 40 Building ahead and stockpiling of motors is possible with a cost of $55 per month. Orders that are not shipped in the month requested are subject to a contractual penalty of $80 per month. At the end of June all orders need to be satisfied. Formulate an LP problem that can determine a production schedule to meet the demands for the motors with the minimum total of shipping, storage, penalty and production differential costs.