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Constrained optimization problem You are an employee with an hourly wage of 40 dollars and you can work up to 24 hours per day. You

Constrained optimization problem

  • You are an employee with an hourly wage of 40 dollars and you can work up to 24 hours per day. You also make key chains at home as hobby. You can make 5 key chain for each you spend crafting and you can spare up to 24 hours for your hobby in a day. You sleep 7 hours everyday.
  • Suppose your utility function for consumption of a good x with price of 1 and keychains made k is: u (x, k) = x + 80 ln(k)

  1. Find the equation for a budget constraint, time constraint and production function for keychains. Denote the hours spent making keychains as hk and the hours spent working as hw.
  2. How many hours should you spend making keychains and how many keychains do you make? How many hours do you spend working?

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