Question

Isa owns a parking garage in downtown Colombia. He charges $5.00 per hour. The company has total costs of $550 when 50 parking stalls/spots are occupied and $650 when 100 parking stalls/spots are occupied within the hour. Find the profit function of the company operating this parking package. Note: Assume the functions are linear.

Answer 1

We have the following information

Per hour parking charge = $5

The company has total costs of $550 when 50 parking stalls/spots are occupied

The company has total costs of $650 when 100 parking stalls/spots are occupied within the hour

So, total cost (TC) function will be of the following form

TC = 300/X + 5P                                    X = 1 for P = 50, and X = 2 for P = 100

P = Parking stalls/spots

When P = 50

TC = 300/1 + (5 × 50)

TC = 300 + 250

TC = $550

When P = 100

TC = 300/2 + (5 × 100)

TC = 150 + 500

TC = $650