Question
a farmer wishes to fence off a rectangular plot of land, using an existing wall as one of the sides . the total are enclosed must be 600 square yards. the fence on the side parallel to the wall will cost 20$ per yard, while the fences on the other side will cost 30$ per yard.
What should the dimension of the rectangle be in order to minimize the total cost of the fence?
What should the dimension of the rectangle be in order to minimize the total cost of the fence?
Answers
Reiny
let the two equal width be x
let the single side by y
xy = 600
y = 600/x
cost = 20y + 30x
= 20(600/x) + 30x
d(cost)/dx = -12000/x^2 + 30
= 0 for a min of cost
30 = 12000/x^2
x^2 = 400
x = 20
the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.
let the single side by y
xy = 600
y = 600/x
cost = 20y + 30x
= 20(600/x) + 30x
d(cost)/dx = -12000/x^2 + 30
= 0 for a min of cost
30 = 12000/x^2
x^2 = 400
x = 20
the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.