Quandaries and Queries


A company that sells x units of a product generates an income (I, in dollars) which is a function of x. The income generated is described by the equation

I = (-1/2)x2 + 100x.

Discuss how to determine the number of units that must be sold so that the company can maximize its income. What is the maximum income?



Hi Connie,

I am not sure what is expected but I would sketch a graph of the function

I = (-1/2)x2 + 100x.

You can solve

(-1/2)x2 + 100x = 0

to see where the graph crosses the x-axis, and then either sketch a few points or use the fact that the graph is a parabola that opens downward to sketch the graph.

From the graph you can see the value of x that maximizes the income.



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