55
QuizMultiple Choice

Quadratic Functions and Equations in Financial Context — Quiz

Question 55 • Financial Math

The revenue function for a new tech gadget is R⁡(x)=−0.051⁢x^2+679⁢x The table shows various costs depending on the number of units produced. Units Cost ( $ ) 1,000 930,000 5,000 2,210,000 Write the linear cost function so that x is the number of units produced. What is the larger number of units that need to be sold to break even? Round your answer to the nearest whole number.

Answer
A
3 comma 520 units
B
4 comma 173 units
C
2 comma 000 units
D
21 comma 770 units

Explanation

The cost function is linear. Its slope is (2,210,000 − 930,000) ÷ (5,000 − 1,000) = $320 per unit, so using the first data point gives C(x) = 320x + 610,000. Set revenue equal to cost: −0.051x² + 679x = 320x + 610,000. The larger solution is about 4,172.94, which rounds to 4,173 units, so the answer is 4,173 units.

AI-written and checked against the verified answer.

Previous
Next