Question 1128209
Maximum profit: A kitchen appliance manufacturer can produce up to 200 appliances per day. The profit made from the sale of these machines can be modeled by the function P(x)=-0.5x^2+175x-3300 where P(x) is the profit in dollars, and x is the number of appliances made and sold.

a)Find the y intercept and explain what it means in this context.
b)Find the x intercepts and explain what they mean in this context.
c)Determine the domain of the function and explain its significance.
d)How many should be sold to maximize profit? What is the maximum profit?
<pre>To find the x-intercepts, you don't have to take the COMPLEX approach as the other person did.
Profit equation: {{{matrix(4,3, f(x), "=", - .5x^2 + 175x - "3,300", 
0, "=", - .5x^2 + 175x - "3,300",
- 2(0), "=", - 2(- .5x^2 + 175x - "3,300"),
0, "=", x^2 - 350x + "6,600")}}}
(x - 330)(x - 20) = 0
As seen above, the x-intercepts are: {{{highlight_green(matrix(1,3, 330, and, 20))}}}
d1) Also, maximum units for maximum profit is realized at the point where {{{matrix(1,3, x, "=", - b/(2a))}}}, or where: {{{matrix(1,5, x, "=", - 175/(2 * - .5), "=", 175)}}}
d2) Maximum profit occurs at: {{{highlight_green(matrix(1,5, f(175), "=", - .5(175)^2 + 175(175) - "3,300", "=", highlight("$12,012.50")))}}}