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.

Algebra ->  Polynomials-and-rational-expressions -> 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.       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
36x%5E2%2B1875x-6500

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

Vertex:
x value, -1875%2F%282%2A36%29=-1875%2F72=-625%2F24


Roots-Zeros
discriminant 1875%5E2%2B4%2A36%2A6500=4451625=3%2A3%2A3%2A5%2A5%2A5%2A1319=9%2A25%2A15%2A1319
-
x=%28-1875%2B3%2A5%2Asqrt%2815%2A1319%29%29%2F72
x=%28-625%2B5%2Asqrt%2819785%29%29%2F24
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.