Question

The profit function for a certain commodity is given by () = 110 − 2 − 1000. Find the level of production that yields maximum profit and hence find the maximum profit.

Answer 1

Based on the profit function given, the level of production that yields the maximum profit is 55 units. The maximum profit is $2,025.

What is the maximum profits unit?

With a profit function:

=-x² + 110x - 1,000

Using a parabola function, we know:

= -b / 2a

The maximum units is:

= -110 / (-2 x 1)

= 55 units

The maximum profit is:

= -(55)² + (110 x 55) - 1,000

= $2,025

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