You have decided to build a rectangular vegetable garden of area A. To protect your vegetables from rabbits and deer, you need to build a fence around your garden. The north side of your garden will be your house (that is, you do not need to build a fence on that side), the east and west side of your garden will each have a fence of length W, and the south side will have a fence of length L. One meter of fence costs p dollars. 10. Write down the optimization problem as an optimization problem with a single variable, W. Hint: find L from the area formula A = WL, and replace it in the objective function. If you cannot solve question 10, then write down I am using the given formula as your answer to question 10, and assume for the rest of this section that the optimization problem is min W Note: I will not accept the above formula as the answer to question 10 (it is incorrect!), and you do not get any points for question 10. 11. Write down the first order condition for this problem. Do not solve the equation yet! Use the first order condition and the Implicit Function Theorem to calculate @W*/@c and W*/8A , where W* is the optimal length of the south fence of your garden. 13. Write down and check the second order condition(s). {w}C(W + ). 12. Assume A=50m2 and your house's length is 7 meters. That is, the length of the south fence of your house cannot exceed 7 meters. 14. Find the optimal dimensions of your garden