SOLUTION: Help me solve this problem: The profit function for a company is P(x) = 36x^2 + 1875x � 6500 where Profit is in dollars, and x represents the number of widgets manufactured.

Question 1124737: Help me solve this problem:
The profit function for a company is P(x) = 36x^2 + 1875x � 6500 where Profit is in dollars, and x represents the number of widgets manufactured.

(a) The profit function is a quadratic function. Does the function 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) What are the minimum start-up costs? Justify your answer.

(e) Find and interpret the break-even point. Show algebraic work.

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!

Opens upward. Look for zeros or the break-even points, P(x)=0; solve for x.

Vertex:
x value,

Roots-Zeros
discriminant
-

x
is about 3.262.
Only nonzero whole number is allowed.
No profit at 3 units
Any profit begins at 4 units for x.
Profit only increases for any whole number x greater than 4 units.

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