The Meyers Company produces small engines for several manufacturers. The company receives orders from two assembly plants for their Top-flight engine. Plant 1 needs at least 45 engines, and plant 2 needs at least 32 engines. The company can send at most 120 engines to these two assembly plants. It costs $30 per engine to ship to plant 1 and $40 per engine to ship to plant 2. Plant 1 gives Miers $20 in rebates toward its products for each engine they buy, while plant 2 gives similar

$15 rebates. Miers 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?