An operations manager is trying to determine a production plan for the next week. There are three products (say, P, Q, and R) to produce using four machines (say, A, B, C, and D). Each of the four machines performs a unique process. There is one machine of each type, and each machine is available for 2400 minutes per week. The unit processing times for each machine is given below. Machine Unit Processing Time (min) Product P Product Q Product R 20 10 A 10 B 12 28 16 Availability (min) 2400 2400 2400 2400 15 6 16 D 10 15 0 Total processing time 57 59 42 9600 The unit revenues and maximum sales for the week are indicated below. Storage from one week to the next is not permitted. The operating expenses associated with the plant are $6000 per week, regardless of how many components and products are made. The $6000 includes all expenses except for material costs. Item Product P Product Q Product R Revenue per unit $90 $100 $70 Material cost per unit $45 $40 $20 Profit per unit $50 Maximum sales 100 40 60 $45 $60 Here we seek the "optimal product mix-- that is, the amount of each product that should be manufactured during the present week in order to maximize profits. Formulate this as an LP