Math: Calculus
posted by REALLY NEED HELP!!! .
A fence is to be built to enclose a rectangular area of 230 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

My dimensions that I got is sqrt(215.625)*230/sqrt(215.625) but it's wrong.

cost = 5(2b+L) + 15 L = 10 b + 20 L
bL = 230 so b = 230/L
cost = 2300/L + 20 L
d cost/dL = 2300/L^2 + 20 L
= 0 for min
20 L = 2300/L^2
L ^3 = 115
L = 4.86
b = 47.3
check my arithmetic !!! 
cost = 5(2b+L) + 15 L = 10 b + 20 L
bL = 230 so b = 230/L
cost = 2300/L + 20 L
d cost/dL = 2300/L^2 + 20 *******
= 0 for min
20 = 2300/L^2
L ^2 = 115
L = 10.72
b = 21.5
b = 47.3 
cost=5*(2w+L)+15L
Area= Lw or w= ARea/L=230/L
cost= 10(230/L)+5L+15L
dcost/dL= 2300/L^2+20=0
L=sqrt 115 and w= 230/sqrt115
Respond to this Question
Similar Questions

Calculus
A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the … 
calculus
A fence is to be built to enclose a rectangular area of 210 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the … 
Math
A fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the … 
Calculus 1
A fence is to be built to enclose a rectangular area of 220 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the … 
Calculus  Optimization
A fence is to be built to enclose a rectangular area of 800 square feet. The fence along 3 sides is to be made of material $4 per foot. The material for the fourth side costs $12 per foot. Find the dimensions of the rectangle that … 
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 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 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the … 
Math
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 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the … 
Math 115
A fence is to be built to enclose a rectangular area of 320 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the …