Question

4. The revenue of a company for a given month is represented as ????(x) = 1,500x − x^2 and its costs as ????(x) = 1,500 + 1,000x.

What is the selling price, x, of its product that would yield the maximum profit? Show or explain your answer.

Answer 1

The profit will be maximum on x = 250.

Explanation:

From the given information:

Revenue = 1500x - x²

Cost = 1500 + 1000x

As we know that

Profit = Revenue - Cost ; Let say it equation 1

Then after putting the values of revenue and cost in equation 1 we have:

Profit = (1500x - x²) - (1500 + 1000x)

Profit = 1500x - x² - 1500 - 1000x

Profit = -x² + 500x - 1500

We know that at the max or min the slope of the graph formed by the profit function will be zero, therefore we find the slope of profit function by taking the first derrivative w.r.t. x as under:

d(Profit)/dx = d/dx(-x² + 500x - 1500)

d(Profit)/dx = -2x + 500

By putting the above slope equal to zero we get:

d(Profit)/dx = -2x + 500 = 0

-2x + 500 = 0

-2x = -500

x = 250

Therefore it is concluded that the profit will be maximum when x will be equal to 250.