Final answer:
The total cost of producing 5 units of output is approximately $323.01.
Step-by-step explanation:
The production function is given by f(L, M) = 4L1/2M1/2, where L represents the number of units of labor and M represents the number of machines used. To calculate the total cost of producing 5 units of output, we need to determine the values of L and M. Since the production function is in terms of L and M, we need to use the inverse function L = f-1(Q) to find the values of L and M at Q = 5.
We have the following table of values:
Widgets (Q)Workers (L)Machines (M)
0.21.002500.42.80510.15940.85.47720.4495160.5025
From the table, we can approximate the values of L and M at Q = 5 to be L ≈ 6 and M ≈ 0.5025. Therefore, the total cost of producing 5 units of output can be calculated as follows:
Total cost = Cost of labor + Cost of machines
Total cost = Number of units of labor × Cost of labor + Number of units of machines × Cost of machines
Total cost = 6 × $49 + 0.5025 × $16
Total cost ≈ $314.97 + $8.04
Total cost ≈ $323.01