The Miers Company makes small engines for many manufacturers. Company receives orders from 2 assembly plants for the engine. Plant I requires at least 50 engines, and plant II requires at least 27 engines. Company can send at most 105 engines to the two assembly plants. It costs given amount $ 20 per engine to ship to plant I and given amount $ 35 per engine to ship to plant II. Plant I provides Miers $ 15 in rebates toward the products for every engine Miers buys, where as plant II provides similar $ 10 rebates. Miers evaluates that it requires at least $ 1200 in rebates to cover products it plans to purchase from two plants. How many engines must be shipped to every plant to minimize shipping costs? Determine the minimum cost?