Vinny's company customizes and sells hats. The function p(x)=−10x2+700x−6000 , graphed below, indicates how much profit he makes in a month as a function of the selling price. What should Vinny charge per hat to make the maximum profit, and what is the maximum profit he can make? (1 point) Responses $6,250 at $35 per hat $6,250 at $35 per hat $7000 at $30 per hat $7000 at $30 per hat $6000 at $40 per hat $6000 at $40 per hat $4850 at $25 per hat
To find the selling price that will maximize Vinny's profit, we need to find the vertex of the parabola represented by the function p(x) = -10x^2 + 700x - 6000.
The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -10 and b = 700 in this case.
x = -700 / (2*(-10)) = -700 / (-20) = 35
Therefore, Vinny should charge $35 per hat to maximize his profit.
To find the maximum profit, we substitute x = 35 into the equation p(x) = -10x^2 + 700x - 6000.
p(35) = -10(35)^2 + 700(35) - 6000 = -12250 + 24500 - 6000 = 6250
So, the maximum profit Vinny can make is $6250.
Therefore, the correct answer is: $6250 at $35 per hat.