Production The production function for a manufacturer is given by
(a) Find the maximum production level for this manufacturer.
(b) Find the marginal productivity of money.
(c) Use the marginal productivity of money to find the maximum number of units that can be produced when $125,000 is available for labor and capital.
(d) Use the marginal productivity of money to find the maximum number of units that can be produced when $350,000 is available for labor and capital.
(a)
To calculate: The maximum production level of the manufacturer from the function
Given Information:
The production function for a manufacturer is given by
Formula used:
Method of Lagrange multipliers,
If the function
Steps to determine the minimum or maximum of the function
1. Solve the system of equations,
Calculation:
Consider the function,
Maximize
constraint.
Since
And
And
Using
(b)
To calculate: The marginal productivity of money from the function
(c)
To calculate: The maximum number of units that can be produce when
(d)
To calculate: The maximum number of units that can be produce when
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