Question

A lighting fixture manufacturer has daily production costs of C = 0.25n^2 - 10n + 800, where C is the total daily cost in dollars and n is the number of light fixtures produced. How many fixtures should be produced to yield a minimum cost? What is the minimum cost?
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Answer 1

Answer:

The minimum value occurs at 20 fixtures and is $700

Step-by-step explanation:

C = 0.25n^2 - 10n + 800

to find the minimum we need to find the vertex

this parabola opens upwards, so the minimum is at the vertex

the vertex is at h=-b/2a  where an^2 +bn+c

h = -(-10)/2*.25

h = (10/.5)

h= 20

the n value of the vertex is at 20

the find the C value, we substitute this into the equation

c(20) = .25 (20)^2 -10(20) + 800

C(20) = .25 (400) - 200 + 800

C(20) = 100 -200+800

C(20) = 700

The minimum value occurs at 20 fixtures and is $700