Suppose you have 74 feet of fencing to enclose a rectangular dog pen. the function A=37x-x^2, where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area?

A). width = 37ft; area = 721.5

B). width = 18.5ft; area = 342.3

C). width = 37ft; area = 342.3

D). width = 18.5ft; area = 1026.8

Question

Mathematics

Giselle Sutton

23 July, 21:44

Suppose you have 74 feet of fencing to enclose a rectangular dog pen. the function A=37x-x^2, where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area?

A). width = 37ft; area = 721.5

B). width = 18.5ft; area = 342.3

C). width = 37ft; area = 342.3

D). width = 18.5ft; area = 1026.8

+3

Answers (1)

Know the Answer?

Jae · Answer 1

To solve for the maximum area, the first derivative should be solved and equate it to zero, then solve for x.

A = 37x - x^2

dA / dx = 37 - 2x

equate dA / dx = 0

0 = 37 - 2x

2x = 37

x = 37 / 2

x = 18.5 ft

so the maximum area is

A = 37x - x^2

A = 37 (18.5) - 18.5^2

A = 342.25 sq ft

so the answer is letter B