Question

The highway department is planning to build a picnic area for motorist along a major highway. It is to be rectangular with an area of 5000 sq. m is to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing that will be needed to complete the job?
a. 500m
b. 300m
c. 200m
d. 400m

Answer 1

F(x) = 2w + I  = 2w  5000/w

f'(x) = 2 - 5000 / w^2

Fencing is minimum, so f(x) = 0

2 - 5000/w^2 = 0

2 = 5000 /w^2

2w^2 = 5000

w = 50

I = 5000/2 

= 1000

2w  + I  
= 200

hope this helps