To find the price per chair that will maximize David's profit, we need to find the vertex of the quadratic function p(x) = -10x^2 + 100x - 210. The x-coordinate of the vertex represents the price per chair that will maximize the profit.
To find the vertex, we can either use the formula x = -b/2a or complete the square. Let's use the formula x = -b/2a since it's simpler in this case.
From the given function p(x) = -10x^2 + 100x - 210, we can see that a = -10 and b = 100. Plugging these values into the vertex formula:
x = -100 / (2 * -10)
x = -100 / -20
x = 5
So, the price per chair that will maximize the profit is $5.
To find the maximum profit, we substitute the value of x = 5 back into the function p(x):
p(5) = -10(5)^2 + 100(5) - 210
p(5) = -250 + 500 - 210
p(5) = 40
Hence, the maximum profit David can make in a month is $40.
Therefore, the correct answer is a) $40 at $5 per chair.