SOLUTION: A company determines that its total cost is given by the function C(x) = 2.5x^2 - 125x + 10,000 where x is the number of units produced and C(x) is in dollars. A. How man

Algebra ->  Finance -> SOLUTION: A company determines that its total cost is given by the function C(x) = 2.5x^2 - 125x + 10,000 where x is the number of units produced and C(x) is in dollars. A. How man      Log On


   

Question 154220: A company determines that its total cost is given by the function
C(x) = 2.5x^2 - 125x + 10,000 where x is the number of units produced and C(x) is in dollars.
A. How many units mut be produced to minimize cost?
B. What is the minimum cost?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A company determines that its total cost is given by the function
C(x) = 2.5x^2 - 125x + 10,000 where x is the number of units produced and C(x) is in dollars.
:
A. How many units must be produced to minimize cost?
:
In a quadratic equation, we can find the axis of symmetry to find at what value of x, c is minimum:
:
Axis of symmetry: x = -b%2F%282a%29
In this equation a=2.5; b+ -125
:
x = %28-%28-125%29%29%2F%282%2A2.5%29 = 125%2F5
x = 25 units will give minimum cost
;
;
B. What is the minimum cost?
:
Find min cost by substituting 25 for x in the given equation:
C(x) = 2.5(25^2) - 125(25) + 10000
C(x) = 2.5(625) - 3125 + 10000
C(x) = 1562.5 - 3125 + 10000
C(x) = $8437.50 is the minimum cost