You have decided to build a rectangular garden of area A. The east and west sides...

 

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You have decided to build a rectangular garden of area A. The east and west sides 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 labor). Note that A, L, and C are exogenous variables, you can only choose b and h. (a)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. (b) Write down the first-order condition for your problem. Do not solve it yet! (c) Find the critical value(s) for b. (d) Write down the second-order condition(s) and verify whether it they are satisfied. You have decided to build a rectangular garden of area A. The east and west sides 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 labor). Note that A, L, and C are exogenous variables, you can only choose b and h. (a)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. (b) Write down the first-order condition for your problem. Do not solve it yet! (c) Find the critical value(s) for b. (d) Write down the second-order condition(s) and verify whether it they are satisfied.

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a The area of the rectangular garden is given by A bh where b is the length of the east and west sid... View the full answer