Sam and Erica are starting a new restaurant in Portland,Oregon.While Sam plans to do the cooking himself,he will need to employ workers and machinery to produce food.He estimates his production function as:
q = 15L.²⁵K
Sam is able to accumulate $10,000 to finance the business.Workers cost $10 and capital costs $50.
a.If Sam wishes to produce the most output with the finances available,how much labor and capital should Sam employ? Use a Lagrangian to solve this problem.
b.Does this bundle of capital and labor also minimize the costs? Explain using a graph.

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The Answer of Sam and Erica are starting a new restaurant in Portland,Oregon.While Sam plans to do the cooking himself,he will need to employ workers and machinery to produce food.He estimates his production function as:
q = 15L.²⁵K
Sam is able to accumulate $10,000 to finance the business.Workers cost $10 and capital costs $50.
a.If Sam wishes to produce the most output with the finances available,how much labor and capital should Sam employ? Use a Lagrangian to solve this problem.
b.Does this bundle of capital and labor also minimize the costs? Explain using a graph.

Sam and Erica Are Starting a New Restaurant in Portland,Oregon