A division of Ditton Industries manufactures a deluxe toaster oven. The daily ma

Question

A division of Ditton Industries manufactures a deluxe toaster oven. The daily marginal profit function associated with the production and sales of the deluxe toaster ovens is known to be P'(x) = 0.0003x2 + 0.06x + 21 where x denotes the number of units manufactured and sold daily and P'(x) is measured in dollars per unit. Management has determined that the daily fixed cost incurred in the production is $800. (a) Find the total profit realizable from the manufacture and sale of 200 units of the toaster ovens per day. Hint: P(200) P(0) = 200 P'(x) dx, 0 P(0) = 800. $ (b) What is the additional daily profit realizable if the production and sale of the toaster ovens are increased from 200 to 220 units/day?

Explanation / Answer

a) P(200) P(0) = 200 P'(x) dx

P(0) = -800

P(200) + 800 = 200 P'(x) dx

P(200) = 200 ( - 0.0003 (200)^2 + 0.06 *200 + 21) - 800

P(200) = 3400$

b) P(220) - P(200) = 20 P'(x)

P(220) - 3400 = 20 (  - 0.0003 (20)^2 + 0.06 *20 + 21)

P(220) = 3841.6$

or Profit = 441.6$

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