Max makes and sells posters. The function p(x) = –10x2 + 200x – 250, graphed below, indicates how much profit he makes in a month if he sells the posters for 20 – x dollars each. What should Max charge per poster to make the maximum profit, and what is the maximum profit he can make in a month? (1 point) Responses $800 at $10 per poster $800 at $10 per poster $800 at $5 per poster $800 at $5 per poster $750 at $10 per poster $750 at $10 per poster $750 at $5 per poster $750 at $5 per poster Skip to navigation
To find the price that Max should charge per poster to make the maximum profit, we need to find the x-value of the vertex of the quadratic function p(x) = -10x^2 + 200x - 250.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -10 and b = 200.
x = -200 / (2*-10)
x = -200 / -20
x = 10
Therefore, Max should charge $10 per poster to make the maximum profit.
To find the maximum profit he can make in a month, we substitute the x-value of the vertex into the profit function p(x).
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.
The correct answer is: $750 at $10 per poster.