Question

The weekly revenue for a company is r= -4p^2 + 50p +1017 , where p is the price of the company’s product. Use the discriminate to find whether there is a price for which the weekly revenue would be $2000.

Answer 1

To find out if there is a price for which the weekly revenue would be $2000, we need to set up the equation:

-4p^2 + 50p +1017 = 2000

Rearrange the equation to form a quadratic equation in standard form:

-4p^2 + 50p + 1017 - 2000 = 0

Simplify:

-4p^2 + 50p - 983 = 0

Now we have a quadratic equation in the form of:

ap^2 + bp + c = 0

where a = -4, b = 50, and c = -983.

To determine whether there is a price for which the weekly revenue would be $2000, we need to find the discriminant, which is given by the formula:

D = b^2 - 4ac

Substituting the values from our equation, we have:

D = 50^2 - 4(-4)(-983)

D = 2500 - 15728

D = -13228

Since the discriminant is negative (D < 0), there are no real solutions to the equation. Therefore, there is no price for which the weekly revenue would be $2000.