Question: The Cobb-Douglas production function for a product is P = 5L 0.8 K 0.2 , where P is the quantity produced, L is the size

The Cobb-Douglas production function for a product is

P = 5L^0.8K^0.2,

where P is the quantity produced, L is the size of the labor force, and K is the amount of total equipment. Each unit of labor costs $300, each unit of equipment costs $100, and the total budget is $15,000.
(a) Make a table of L and K values which exhaust the budget. Find the production level, P, for each.
(b) Use the method of Lagrange multipliers to find the optimal way to spend the budget.

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