A company has the Cobb-Douglas production function 
, where x is the number of units of labor, y is the number of units of capital, and z is the units of production. Suppose labor costs $200 per unit, capital costs $200 per unit, and the total cost of labor and capital is limited to $400000. Find the number of units of labor and the number of units of capital that maximize production.
Definitions:
Internal Rate
Often refers to the internal rate of return (IRR), a metric used in capital budgeting to estimate the profitability of investments.
Present Value
The current worth of a future sum of money or stream of cash flows, given a specified rate of return.
NPV Decision Rules
Guidelines used to determine the viability of an investment or project based on the Net Present Value, which calculates the present value of cash inflows minus the present value of cash outflows.
Shareholder Wealth
The total value of a company to its shareholders, typically measured by the market capitalization or the equity value of the company.
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