You have decided to build a rectangular garden of area A. The east and west side of the garden will require a fence of length h, and the south side of the garden requires a fence of length b. Since your house will be on the north side of your garden. the north fence of your garden will require a fence of length b - L. where L is the length of your house. A meter of fence costs C dollars to install [that includes materials and labouri. Note that A, L and C are exogenous yariables, you can only choose b and h. '1. Write down the optimization problem you are faced with as an optimization problem with a single variable, I. Hint: solve the area equation bh = A for h, and plug the result for h into your objective function. 2. Write down the first order condition for your problem. Do not solve it yet! . Find the critical yaluels} for b. 4. Write down the second order conditionlsi and verify whether itfthey are satisfied. m 5. Use the first order condition with the Implicit Function Theorem to calculate the derivatives of the critical value of b with respect to each of the exogenous variables of your model. Note that you are not allowed to use your answer to question 3 to calculate those deriyatiyes. You have to use the Implicit Function Theorem