"a manufacturing company receives orders for engines from two assembly plants. plant i needs at least 45 engines, and plant ii needs at least 32 engines. the company can send at most 140 engines to these assembly plants. it costs $30 per engine to ship to plant i and $50 per engine to ship to plant ii. plant i gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant ii gives similar $15 rebates. the manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. how many engines should be shipped to each plant to minimize shipping costs? what is the minimum cost? "