SOLUTION: A factory produces skateboards. The cost of producing x hundreds of units a day can be approximated by the formula C = 0.89x^2 - 9.32x + 3677. Find the daily production level that

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A factory produces skateboards. The cost of producing x hundreds of units a day can be approximated by the formula C = 0.89x^2 - 9.32x + 3677. Find the daily production level that       Log On


   

Question 211214: A factory produces skateboards. The cost of producing x hundreds of units a day can be approximated by the formula C = 0.89x^2 - 9.32x + 3677. Find the daily production level that will minimize the cost.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The cost (C) of producing x-hundreds of skateboards a day is given by:
C+=+0.89x%5E2-9.32x%2B3677
The minimum point of this equation (a parabola) occurs at the vertex of the parabola. The x-coordinate of the vertex of this parabola is given by:
x+=+%28-b%29%2F2a where a = 0.89, and b = -9.32, so...
x+=+%28-%28-9.32%29%29%2F2%280.89%29 Evaluate.
x+=+5.24 Rounded to the nearest hundreth.
Since x is in hundreds of skateboards, multiply this by 100 to get:
A daily production level of 524 skate boards daily will minimize the cost.