Question 1135433: 13. (18 pts) The cost, in dollars, for a company to produce x widgets is given by
C(x) = 4050 + 9.00x for x ≥ 0, and the price-demand function, in dollars per widget, is p(x) = 63-0.03x for 0 ≤ x ≤ 2100.
In Quiz 2, problem #10, it was seen that the profit function for this scenario isP(x) = -0.03x^2 + 54.00x-4050.
(a) The profit function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? __________
(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work.
(c) State the maximum profit and the number of widgets which yield that maximum profit:
The maximum profit is _____________, when ___________ widgets are produced and sold. (d) Determine the price to charge per widget in order to maximize profit.
(e) Find and interpret the break-even points. Show algebraic work.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
The cost, in dollars, for a company to produce x widgets is given by
 for  , and
the price-demand function, in dollars per widget, is
 for
In Quiz 2, problem #10, it was seen that the profit function for this scenario is
(a) The profit function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? ___ _______
(b) Find the vertex of the profit function P(x) using algebra.
 ...complete square
recall: 
since  , we have  ...solve for 
then we have
=> and 
vertex is at: ( , )
(c) State the maximum profit and the number of widgets which yield that maximum profit:
The maximum profit is _____ ________, when ___ ________ widgets are produced and sold.
(d) Determine the price to charge per widget in order to maximize profit.
...plug in
(e) Find and interpret the break-even points. Show algebraic work.
Break-Even _Point => when 
if
then 
 ...using quadratic formula we get:
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