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Question:

The inventor of a new product believes that the cost of producing the product is given by the function C(x) = 1.75x + 7000. If the inventor charges $4 per unit, then her profit for producing and selling x units is given by the function P(x) = 2.25x – 7000
(a) What is her profit if she sells 2000 units?
A) $10,500 B) $3,500 C) -$2,500

(b) What is her profit if she sells 5000 units?
A) $4,250 B) $8,750 C) -$2,000

(c) What is the break-even point for sales stated in the number of units?
A) 3,500B) 3,112C) 7,000

Answer:
A. x = 2000, substitute this into the profit equation:
P(2000) = 2.25(2000) - 7000 = -2500

B. x = 5000, substitue this into the profit equation also:
P(5000) = 2.25(5000) - 7000 = 4250

C. Break-even point is where the profit = 0, so set that equation = 0 and solve for x.
0 = 2.25x - 7000
7000 = 2.25x
7000/2.25 = x
x = 3111.11 or 3112 units.

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