Question

The revenue function for a real estate agency is based on a percentage of the amount of monthly sales made by agents. The cost function for the agency is based on the commissions, paid to the agent plus the fixed monthly costs. both functions are shown below where X is the dollar amount of the monthly sales made by agents.

• Revenue function: f (x) = 0.03
• Cost function: g (x) = 0.015x + 4,600
The agency will break, even when the revenue function is equal to the cost function. For the agency to break even, what amount of monthly transactions, in dollars, must be generated by its agents?

• Between $0 and $2000
• Between $4,500 and $4,700
• Between $153,000 and $155,000
• Between $305,000 and $307,000

Answer 1

D. Between $305,000 and $307,000

Explanation:

A. This is a result of finding 4,600(0.03 + 0.015).

B. This is a result of using the y-intercept for the cost function.

C. This is a result of incorrectly solving the equation 0.03x = 0.015x + 4,600 by dividing 4,600 by 0.03

instead of 0.015 in the final step.

D. This is a result of correctly solving the equation 0.03x = 0.015x + 4,600 ⇒ 0.015x = 4,600 then dividing

4,600 by 0.015 to get approximately 306,667.