SOLUTION: A soft-drink manufacturer has daily production costs of C = 70,000 - 120x + 0.055x^2 where C is the total cost (in dollars) and x is the number of units produced. How many un

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A soft-drink manufacturer has daily production costs of C = 70,000 - 120x + 0.055x^2 where C is the total cost (in dollars) and x is the number of units produced. How many un      Log On


   



Question 4789: A soft-drink manufacturer has daily production costs of
C = 70,000 - 120x + 0.055x^2
where C is the total cost (in dollars) and x is the number of units produced. How many units should be produced each day to yield a minimum cost?

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This graph is actually a parabola opening upward. The minimun cost will occur at the vertex, which is at x+=+%28-b%29%2F%282a%29+, where a is the coefficient of x%5E2 and b is the coefficient of x. In this case, a=0.055 and b= -120.

Minimum cost = 120%2F%282%2A0.055%29 =120%2F0.11= 12000%2F11 = 1090.9 or 1091 units.

Things usually come out better than that, but then life doesn't always come out even, does it?

R^2 at SCC