A product may be made using Machine I or Machine II. The manufacturer estimates that the monthly fixed costs of using Machine I are $19,000, whereas the monthly fixed costs of using Machine II are $15,000. The variable costs of manufacturing 1 unit of the product using Machine I and Machine II are $13 and $19, respectively. The product sells for $60 each.

(a) Find the cost functions C(x) associated with using each machine, where x is the number of units produced using that machine.

(b) Sketch the graphs of the cost functions of part (a) and the revenue function on the same set of axes. (Sketch the graphs using rays.)

(c) Which machine should management choose to maximize their profit if the projected sales are 450 units?

Which machine should management choose to maximize their profit if the projected sales are 550 units?

Which machine should management choose to maximize their profit if the projected sales are 650 units?

(d) What is the profit for each case in part (c)?

450:

550:

650: