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You are designing a rectangular dog pen off the back of your house. The House will form one side of the dog pen. The pen is to have an area of 800 ft.² but you want to minimize the amount of fencing that you need for the three sides of the pen not against the house. This will include an opening that it's 4 feet wide where it will be placed. How many feet of fencing do you need to build the pen?

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  1. xy = 800
    f = x+2y-4

    To minimize p, substitute in for x or y, and find where p'=0.

    Check to be sure it does not matter where the gate is. (on the x side or the y side)

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