SOLUTION: A manufacturer estimates that the total cost of producing x items per day is given by the function C(x)=0.01x^2-4x+1500 with C in dollars. How many items should be produced each d

Question 167387: A manufacturer estimates that the total cost of producing x items per day is given by the function C(x)=0.01x^2-4x+1500 with C in dollars. How many items should be produced each day so that the cost will be a minimum? What will be the minimum cost?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
C(x)=0.01x^2-4x+1500
.
Since the coefficient associated with the x^2 term is "positive" (think happy face), the parabola will open upward like a U. Knowing this, if we find the vertex, we'll find the minimum.
.
The axis of symmetry is the line x = -b/2a
.
x = -(-4)/2(0.01)
x = 4/0.02
x = 200 (items produced to minimize cost)
.
To find the cost, plug the value above back into:
C(x)=0.01x^2-4x+1500
C(200)=0.01(200)^2-4(200)+1500
C(200)=400-800+1500
C(200)=-400+1500
C(200)=$1100 (minimum cost)

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