Answer:
L = 6.33 foot
W = 31.62 foot
Step-by-step explanation:
costing of one side is $21 per foot and the costing of other three sides is $ 7 per foot.
Area of rectangular garden, A = 200 ft²
Let L is the length of the garden and W is the width of the garden.
A = L x W
200 = L x W .... (1)
Total cost of fencing is
C = 21 x L + 7 ( 2L + W)
C = 35 L + 7 W .... (2)
Substitute the value of W from equation (1) in equation (2)
[tex]C = 35 L + 7\times \frac{200}{L}[/tex]
[tex]C = 35 L + \frac{1400}{L}[/tex]
Differentiate with respect to L on both the sides:
[tex]\frac{dC}{dL} = 35 - \frac{1400}{L^{2}}[/tex]
Put it equal to zero for maxima and minima
[tex]35 - \frac{1400}{L^{2}}=0[/tex]
L = 6.33 foot
W = 31.62 foot
So, the cost of fencing is minimum when L = 6.33 foot , W = 31.62 foot
