1. Use Calculus to solve the following problem. To receive credit, you must incl

Question

1. Use Calculus to solve the following problem. To receive credit, you must include: an objective function, a constraint if there is one, appropriate derivative(s), written work to find critical point(s), and work for an appropriate test to determine whether the critical points are the locations of maxima or minima or neither. In addition, be sure to answer the question, with labels on your answers.

Jane is going to put a rectangular vegetable garden in her back yard. She will need to buy fencing to go around three sides of the garden, but the fourth side will use the existing fence at the back of her yard. She would like the garden to be 180 square feet. What should the dimensions of the garden be in order to minimize the amount of new fencing she will have to buy?

Explanation / Answer

Let the length and width be x and y ft respectively

Area = length * width

180 = x y

y = 180 / x

P = 2x + y

P = 2x + (180/x)

P '(x) = 2 -(180/x2)

P '(x) =0

2 -(180/x2)=0

x2=90

x = 9.5 ft

y= 180/x = 18.97ft

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