The required equations computed from the data given are :
- R(x) = 860x - 5x²
- C(x) = 120x + 6000
- P(x) = 740x - 5x² - 6000
- Break even point = 139 gallons and 9 apartment
<u>Given the Parameters</u> :
- Price per apartment, p = - 5x + 860
- x = number of apartments rented
- Fixed cost = 6000
- Maintainance cost per apartment = $120
<u>The Revenue Function, R(x) </u><u>:</u>
- Price per apartment × Number of apartments rented
- (-5x + 860)x ;
- R(x) = 860x - 5x²
<u>The Cost equation, C(x)</u> :
- Fixed cost + Maintenance cost per apartment
- C(x) = 6000 + 120x
<u>The Profit function, P(x)</u> ::
P(x) = R(x) - C(x)
P(x) = 860x - 5x² - (6000 + 120x)
P(x) = 860x - 5x² - 6000 - 120x
P(x) = 740x - 5x² - 6000
<u>Number of apartments required to break even</u> :
At break even ;
P(x) = 0
740x - 5x² - 6000 = 0
Divide through by 5
-x² + 148 - 1200 = 0
<em>Using a quadratic calculator</em> :
The roots are (139.39, 8.60)
Therefore. The company will break even at 139 apartments rented or 9 apartments.
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