Answer: 20 fixtures
Explanation:
There are two methods to getting the number of fixtures to be produced.
Method 1
Given:
C(x) = 800 - 10x +

Re - arranging the function , we have
C(x) =
- 10x + 800
This is a typical quadratic expression , since the coefficient of
is positive , it means that the quadratic expression is a parabola that opens upward. We can therefore find the x - coordinate of the vertex of the parabola to find the number of fixtures that can be produced to yield minimum cost.
The formula for finding the x - coordinate of the vertex is give as

From the expression given , a = 0.25 , b = -10 , substituting into the formula , we have:
x =

x = 10/0.5
x = 20
Therefore , 20 fixtures should be produced each day to yield minimum cost.
METHOD 2
This is the application of differential equation , the question means that we need to find the value of x for which the function is minimum. To do this , we will differentiate the function once with respect to x and equate to zero.
C(x) =
- 10x + 800
differentiating once , we have
(x) = 0.5x - 10
setting it to zero , we have
0.5x - 10 = 0
0.5x = 10
x = 10/0.5
x = 20
This means that 20 fixtures should be produced each day to yield minimum cost.