A company knows that if it sets the price of a product at p dollars, the number of units sold will be x million, where p = 2 - x. If the cost of the product is given by 0.25 + 0.5x million dollars. What price should be set to make a profit of $ 0.25 million?

Explanation:

x = number of products, in millions, sold

p = price per product

R = revenue

R = (number of products sold)*(price per product)

R = x*p

R = x(2-x)

R = 2x-x^2

C = costs

C = 0.25 + 0.5x

F = profit

F = revenue - costs

F = R - C

F = (2x - x^2) - (0.25 + 0.5x)

F = -x^2 + 1.5x - 0.25

We want a profit of 0.25 million, so plug in F = 0.25 and solve for x

F = -x^2 + 1.5x - 0.25

0.25 = -x^2 + 1.5x - 0.25

0 = -x^2 + 1.5x - 0.25 - 0.25

-x^2 + 1.5x - 0.5 = 0

Use the quadratic formula to find the two solutions to be x = 0.5 and x = 1

If x = 0.5, then p = 2-x = 2-0.5 = 1.5

If x = 1, then p = 2-1 = 1

There are two price points  (p = 1.5 and p = 1) that lead to the same profit F = 0.25

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

your answer is -9

step-by-step explanation: