Algebra 2 math class work

Question

The per-unit price p (in dollars) of a popular toy when x units (in thousands) are produced is modeled by the function p= 12 - 0.025x. The revenue (in thousands of dollars) is the product of the price per unit and the number of units (in thousands) produced.

So the revenue function is given by r(x) = xp, or rather:

r(x) = x (12 - 0.025x)

According to this function, what is the maximum possible revenue? Type in the number of dollars (without a dollar sign). Be careful, r(x) gives thousands of dollars, not dollars

Answer 1

The revenue function r(x) simplifies to -0.025x² + 12x.

This is a downward-opening parabola (1st term is negative), so there is a revenue maximum at x = -b/2a

That's -12/-0.050 = 240 units. (000's)

Plugging that into the revenue formula, the maximum revenue is $1,440 ($1,440,000).

Check it on the Desmos Graphing Calculator website.