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Suppose that a corporation that manufactures widgets determines that
its revenue function is R(x)=1000x-x^2 and its cost function is C(x)=3000+20x,
where x represents the number of widgets produced.
Find the corporation's maximum profit.
Profit = Revenue - cost
P = (1000x - x^2) - (3000+20x)
P = 1000x - x^2 - 3000 - 20x
P = -x^2 + 980x - 3000;
A quadratic equation, find the axis of symmetry & maximum using x =
In this equation: a=-1; b=980
x = +490 units produce max profit
Find max profit using: P = -x^2 + 980x - 3000;
P = -(490^2) + 980(490) - 3000
P = -240100 + 480200 - 3000
P = $237,100 is max profit
You can check the math by substituting 490 for x in the original equations