A real estate agency has fixed monthly costs associated with rent, staff salarie

Question

A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities, and supplies. It earns its money by taking a percentage commission on total real estate sales. During the month of July, the agency had total sales of $832,000 and showed a net income (after paying fixed costs) of $15,704. In August total sales were $326,000 with a net income of only $523. (a) Use a formula to express net income as a linear function of total sales. Let N be the net income in dollars, and let s be the total sales in dollars. (Round the terms to two decimal places.)

b)Identify the slope and vertical intercept.

c)What are the real estate agency's fixed monthly costs? (Round your answer to two decimal places.)

d)Find the horizontal intercept. (Round your answers to two decimal places.)

Explanation / Answer

For the given data,

Let N = aS + c

At S = 832000, N = 15704

At S = 326000, N = 523

15704 = 832000a + c

523 = 326000a + c

Solving these two equations, we get

a = 0.03

c = -9256

N = 0.03S - 9256

this is of the form y = mx + c

Slope = 0.03

For vertical intercept, S = 0

vertical intercept = -9256

For horizontal intercept, N = 0

horizontal intercept = 308533.33

Fixed monthly cost = $9256

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