Alighting 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? show all of your work!

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

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .