To find the number of units that should be produced each day to yield a minimum cost, we need to determine the value of x that minimizes the daily production cost function C.
The daily production cost function is given by:
C = 400 - 5x + 0.125x^2
To find the minimum cost, we can take the derivative of the cost function with respect to x and set it equal to zero. Then we solve for x.
Taking the derivative of C with respect to x:
dC/dx = -5 + 0.25x
Setting the derivative equal to zero and solving for x:
-5 + 0.25x = 0
0.25x = 5
x = 20
So, the minimum cost will be achieved when 20 units are produced each day.