Question

Tony's Glass Factory makes crystal bowls and has a daily production cost C(x) in dollars given by

C(x) = 0.2x² - 10x + 650, where x is the number of bowls made.

Determine how many bowls should
be made to minimize the production cost? What is the cost when this many bowls are made?

Answer 1

Explanation:

To find this answer you need to find the vertex of the parabola. Do this by using the formulas for h and k as follows:

`h=(-b)/(a)` and
`k=c-(b^2)/(4a)`, where a, b, and c come from the quadratic equation.

Filling in for h:

`h=(10)/(2(.2))=25`

Filling in for k:

`k=650-(100)/(4(.2)) =525`

Thus, the coordinates for the vertex are (25, 525). The h value interprets the number of bowls that should be produced to minimize the cost of production (25) and the minimum production cost is the k value (525).