A manufacturing company receives orders for industrial printers from two factories in Boston and New Orleans. Boston requires at least 45 industrial printers, and New Orleans needs at least 32 industrial printers. The company can send a maximum of 120 industrial printers to these factories. It costs $35 per printer to ship to Boston and $40 per printer to ship to New Orleans. Boston provides the manufacturing company with a $20 rebate for each printer they purchase, while New Orleans offers a $13 rebate. The manufacturer estimates they need at least $1500 in rebates to cover the products they plan to buy from the two factories. How many industrial printers should be shipped to each factory to minimize shipping costs? What is the minimum cost?