Calculus
posted by Catie .
A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area is to be 2484ft^2. The exterior fence costs $18.00 per foot and the interior fence costs $16.50 per foot. Find the dimensions of the pen that will minimize the cost. What is the minimum cost?

if width=x, length=y, the cost=c, we have
xy = 2484
c = 16.50*2x + 18.00*(2x+2y)
= 33x + 36x + 36(2484/x)
= 69x + 89424/x
dc/dx = 69  89424/x^2
dc/dx=0 when x=36
so, the cost is minimum when the pen is 36 by 69.
I assume you can figure the cost.
Respond to this Question
Similar Questions

calc
A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What … 
Calc
A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What … 
Calc
A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What … 
Calculus Word Problem
A farmer wishes to build a fence for 6 adjacent rectangular pens. If there is 600 feet of fencing available, what are the dimensions of each pen that maximizes total pen area? 
Calculus Follow Up
A farmer wishes to build a fence for 6 adjacent rectangular pens. If there is 600 feet of fencing available, what are the dimensions of each pen that maximizes total pen area? 
Calculus
ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the playground is 900 square feet. The fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of … 
Calculus
A fence is to be built to enclose a rectangular area of 310 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 12 dollars per foot. Find the … 
calculus
A rectangular fence has to be built from both wood and metal so that opposite parallel sides of the fence are made from the same type of material. The wood costs $10 per foot and the metal costs $20 per foot of the fence used. If you … 
Math
a 5 foot fence will be built around the perimeter of a 50 foot by 120 foot rectangular lot. if the fence costs $1.80 per linear foot for labor and $.40 per square foot for material, what will be the cost of the fence? 
MATH
A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 50 per foot and the fence for the other two sides will cost20 per foot. The farmer has a total of 2000 dollars to spend …