Question

Max makes and sells posters. the function p(x)=-10x^2+200x-250, graphed below, indicates how much profit he makes in a month if he sells the posters for 20-x dollers each.

what should max charge per poster to make the maximum profit, and what is the maximum profit he can make in a month?

work out

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the charge per poster that maximizes the profit, we need to find the x-coordinate of the vertex of the quadratic function p(x) = -10x^2 + 200x - 250.

The x-coordinate of the vertex is given by x = -b/2a, where the quadratic function is in the form ax^2 + bx + c. In this case, a = -10 and b = 200. Plugging these values into the formula, we get:

x = -200/(2*-10)
x = -200/-20
x = 10

So Max should charge $20 - x = $20 - 10 = $10 per poster to make the maximum profit.

To find the maximum profit, we substitute the value of x = 10 into the profit function p(x) = -10x^2 + 200x - 250:

p(10) = -10(10)^2 + 200(10) - 250
p(10) = -10(100) + 2000 - 250
p(10) = -1000 + 2000 - 250
p(10) = 750

Therefore, the maximum profit Max can make in a month is $750.