A farmer wants to fence in an area of 15000 m² in a rectangular field and then divide it into half with a fence parallel to one sides of the rectangle. How can he do this so as to minimize the cost of the fence?
2 answers
Are you assuming 150 by 100? If so, the amount of fence would be 3(100)+2(150). Compare that to other possibilities, e.g., 300 by 50.
Let the long side by y m
let the shorter side be x m
So the area is xy and xy = 15000, -----> y = 15000/x
For the cost to be minimum , the total amount of fencing has to be minimum
F = 2y + 3x
= 2(15000/x) + 3x
dF/dx = -30000/x^2 + 3
= 0 for a minimum of F
3 = 30000/x^2
x^2 = 10000
x = 100 , then y = 15000/x = 150
State your conclusion
let the shorter side be x m
So the area is xy and xy = 15000, -----> y = 15000/x
For the cost to be minimum , the total amount of fencing has to be minimum
F = 2y + 3x
= 2(15000/x) + 3x
dF/dx = -30000/x^2 + 3
= 0 for a minimum of F
3 = 30000/x^2
x^2 = 10000
x = 100 , then y = 15000/x = 150
State your conclusion
2 answers