The owner of a machine shop is planning to expand by purchasing some new machines-presses and lathes. The owner has estimated that each press purchased will increase profit by $100 per day and each lathe will increase profit by $150 daily. The num- ber of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop. The machine purchase prices and space requirements are as follows. Machine Required Floor Space (ft²) Purchase Price Press Lathe 15 30 $8,000 4,000 The owner has a budget of $40,000 for purchasing machines and 200 square feet of available floor space. The owner wants to know how many of each type of machine to pur- chase to maximize the daily increase in profit. 1 a) Model the problem. b) The owner decided to buy only lathes or press machines. Model the new problem.