Acompany makes two types of sofas, regular and long, at two locations, one in hickory and one in lenoir. the plant in hickory has a daily operating budget of $45,000 and can produce at most 300 sofas daily in any combination. it costs $150 to make a regular sofa and $200 to make a long sofa at the hickory plant. the lenoir plant has a daily operating budget of $36,000, can produce at most 250 sofas daily in any combination and makes a regular sofa for $135 and a long sofa for $180. the company wants to limit production to a maximum of 250 regular sofas and 350 long sofas each day. if the company makes a profit of $50 on each regular sofa and $70 on each long sofa, how many of each type should be made at each plant in order to maximize profit? what is the maximum profit?