Suppose You Adopt A New Puppy And Want To Fence In Your Yard The Side Of Your House Will Be Used As The Boundary On One 1 (54.96 KiB) Viewed 23 times
Suppose You Adopt A New Puppy And Want To Fence In Your Yard The Side Of Your House Will Be Used As The Boundary On One 2 (26.36 KiB) Viewed 23 times
Suppose you adopt a new puppy and want to fence in your yard. The side of your house will be used as the boundary on one side (and not need any fencing on that side). You can afford to purchase 60 feet of fencing material. What are the dimensions of the largest rectangular fence that you can build? Step 1. Introduce variables: Let A be the fenced-in area of your yard, u be length the fence will extend into your yard, and y be the length of the side of house (perpendicular to x). Step 2. State the variable to be maximized and any constraints: We want to maximize with no more than feet of fencing. Step 3. Write an equation for the quantity to be maximized: The area inside the rectangular fence, in terms of u and y, is A= Step 4. Write the equation as a function of one variable: We have a constraint on the amount of fencing 60 We solve this for to obtain y = We substitute this expression into y in the area equation to obtain A= Step 5. Identify the domain: Since the dimensions should not be negative, we know that I > 0 and y 0. However, if at is 60 bigger than then y will be negative. So the domain of x, in interval notation, is 2
Step 5. Identify the domain: Since the dimensions should not be negative, we know that x > 0 and y. However, if u is 60 bigger than then y will be negative. So the domain of x, in interval notation, is 2' 1. Step 6. Locate the maximum: The maximum must occur at a critical value or and endpoint. However, A is zero at the endpoints, so the maximum must occur at feet. The other dimension of the fence must be y = feet.
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