4. An operations manager is trying to determine a production plan for the next week. There are three products (say, P, Q, and Q) to produce using four machines (say, A and 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 in Table 1. Table 1: Machine Data Unit Processing Time (min) Product P Product Q Product R Machine Availability (min) 2400 A 20 10 10 B 12 28 16 2400 15 6 16 2400 D 10 15 0 2400 Total processing time 57 59 42 9600 The unit revenues and maximum sales for the week are indicated in Table 2. 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. Table 2: Product Data Item Product P Product Q $100 Product R $ 70 $90 $45 $ 40 $20 Revenue per unit Material cost per unit Profit per unit Maximum sales $45 $60 $50 100 40 60 The manager would like determine the amount of each product that should be manufactured during the present week in order to maximize profits. After the production plan is determined, a contractor offers to the manager extra machinery time $1 per minute. What do you advice to manager related to the offer? (30 Points)