A manufacturing company gets orders for engines from two assembly plants. Plant I requires at least 45 engines, and plant II requires at least 32 engines. Company can send at most 140 engines to assembly plants. It costs $35 per engine to ship to plant I and $50 per engine to ship to plant II. Plant I provides manufacturing company $20 in rebates toward products for every engine they purchase, where as plant II provides similar $10 rebates. Manufacturer finds that they require at least $1500 in rebates to cover products they plan to purchase from two plants. How many engines must be shipped to every plant to minimize shipping costs? Find minimum cost? How many engines must be shipped to every plant to minimize shipping costs, subject to given constraints?