29. Sally is Skippy\'s neighbor from Exercise 19 in Section 2.3. Sally also want

Question

29. Sally is Skippy's neighbor from Exercise 19 in Section 2.3. Sally also wants to plant a vegetable garden along the side of her home. She doesn't have any fencing, but wants to keep the size of the garden to 100 square feet. What are the dimensions of the garden which will minimize the amount of fencing she needs to buy? What is the minimum amount of fencing she needs to buy? Round your answers to the nearest foot. (Note: Since one side of the garden will border the house, Sally doesn't need fencing along that side.)

Explanation / Answer

Let

length = x feet

width =y feet

Since area is 100,

xy =100

y= 100/x

Find length of fencing as

L= 2x+y

L= 2x +100/x

To minimize find derivative and set to 0 as

2 -100/x² = 0

100/x² = 2

x² = 50

x = 50

x is about 7 feet

y= 100/50 is about 14 feet

hence dimension of garden is about 14 ft by 7 ft

length of fencing = 2*7 +14 = 28 ft

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