23
QuizMultiple Choice

Modeling for Business: Part One — Test

Question 23 • Financial Math

A business owner is trying to determine the break-even point. The owner uses the revenue function R⁡(x)=−0.014⁢x^2+7,000⁢x , and the cost function is C⁡(x)=180,000+2,000⁢x In both functions, x represents the number of units sold. How many units does the owner need to sell to break even? Round to the nearest whole number if necessary.

Answer
A
446 comma 250 units
B
357 comma 107 units
C
180 comma 000 units
D
178 comma 600 units

Explanation

Break-even occurs when revenue equals cost, so set −0.014x² + 7,000x = 180,000 + 2,000x. Rearranging gives 0.014x² − 5,000x + 180,000 = 0, whose solutions are about 36 and 357,107 units. The larger break-even quantity listed is 357,107 units, choice B.

AI-written and checked against the verified answer.

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