The production function for our Production is Q = 25L - 0.05L^2; where Q is output and L is man-hours. What level of man-hours will maximize total output?
To find the level of man-hours that maximizes total output, we can take the derivative of the production function with respect to L and set it equal to zero. This will give us the critical points, one of which will correspond to the maximum output.
Let's start by taking the derivative of the production function:
dQ/dL = 25 - 0.1L
Setting this equal to zero and solving for L, we have:
25 - 0.1L = 0
0.1L = 25
L = 25 / 0.1
L = 250
Therefore, the level of man-hours that maximizes total output is 250.
To find the level of man-hours that will maximize total output, we need to find the value of L where the derivative of the production function with respect to L is equal to zero.
Step 1: Calculate the derivative of the production function with respect to L.
The derivative of Q with respect to L can be found by applying the power rule of differentiation:
dQ/dL = 25 - 0.1L
Step 2: Set the derivative equal to zero and solve for L.
Setting the derivative equal to zero:
25 - 0.1L = 0
0.1L = 25
L = 25 / 0.1
L = 250
Therefore, the level of man-hours that will maximize total output is 250 man-hours.