A manufacturing firm produces two machine parts using lathes, milling machines, and grinding machines. The different machining times required for each part, the machining times available on different machines, and the profit on each machine part are given in the following table. Machining time required (min) Maximum time available Type of machine Lathes Machine part I Machine part II per week (min) 10 5 2500 Milling machines 4 10 2000 Grinding machines 1 1.5 450 Profit per unit $50 $100 - - Determine the number of parts I and II to be manufactured per week to maximize the profit. (20 points) if the profit rates for the machine parts I and II are $40 and $100 instead of $50 and $100, what will be the maximum profit the manufacturing firm can make? Please clearly comment your answer. (10 points)