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?

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Answer 1 · 2016-10-29T01:04:32

The minimum cost would be the #C# coordinate of the vertex. Hence, we will have to complete the square.

#C = 0.25n^2 - 10n + 800#

#C = 0.25(n^2 - 40n) + 800#

#C = 0.25(n^2- 40n + 400 - 400) + 800#

#C = 0.25(n^2 - 40n + 400) - 100 + 800#

#C = 0.25(n - 20)^2 + 700#

The vertex is #(20, 700)#, in the form #(n, C)#, so the minimum cost is #$700#.

Hopefully this helps!