Scanners Cost
How many scanners would produce a maximum profit?
The marketing department of a company estimates that the demand for a color scanner is p=100-0.0001x, where p is the price per scanner and x is the number of scanners. The cost of producing x scanners is C=350,000+30x and the profit for producing and selling x scanners is P=R-C=xp-C. Graphing the profit function, what would be an estimate of the number of scanners that would create a maximum profit?
P = xp-C
P = x(100-0.0001x) - (350000+30x)
P = 100x - 0.0001x² - 350000 - 30x
P = -0.0001x² + 70x -350000
This is a quadratic equation. It forms a parabola shape when you graph it.
If you graph this for x ranging from 0 to 500,000 (in steps of 10,000), you'll notice that the parabola peaks out at around 350,000 and the profit is 11,900,000
I used Excel to do the graphing, but a graphing calculator would do the same thing.
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