12 - 14 Rectangular Lot Problems in Maxima and Minima

Problem 12
A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum?
 

Problem 13
Do Ex. 12 with the words "three lots" replaced by "five lots".
 

Problem 14
A rectangular lot is bounded at the back by a river. No fence is needed along the river and there is to be 24-ft opening in front. If the fence along the front costs \$1.50 per foot, along the sides \$1 per foot, find the dimensions of the largest lot which can be thus fenced in for \$300.
 

09 - 11 Rectangular Lot Problems in Maxima and Minima

Problem 9
What should be the shape of a rectangular field of a given area, if it is to be enclosed by the least amount of fencing?
 

Problem 10
A rectangular field of given area is to be fenced off along the bank of a river. If no fence is needed along the river, what is the shape of the rectangle requiring the least amount of fencing?
 

Problem 11
A rectangular lot is to be fenced off along a highway. If the fence on the highway costs m dollars per yard, on the other sides n dollars per yard, find the area of the largest lot that can be fenced off for k dollars.