Answer:
L = 4 yard, W = 20 yard
Step-by-step explanation:
Area of backyard, A = 80 sq yard
Let the length of the fence is L and the width is W.
The cost of one side is $ 9 per yard and the cost of three sides is $ 1 per yard.
A = L x W = 80
W = 80 / L .... (1)
Total cost, C = L x 9 + L x 1 + 2 W x 1
C = 10 L + 2 W
C = 10 L + 2 (80 / L) from equation (1)
[tex]C = 10 L + \frac{160 }{L}[/tex]
For maxima and minima differentiate C with respect to L and put it equal to zero.
[tex]\frac{dC}{dL}=10-\frac{160}{L^{2}}[/tex]
dC/dL = 0
L² = 16
L = 4 yard
from equation (1)
W = 80 / 4 = 20 yard
SO, the cost is minimum is the length is 4 yard and the width is 20 yard.
