Answer:
to minimize the cost the dimensions should be 340 feet on sides and 170 on the opposite side of the bank
Step-by-step explanation:
Let the length of rectangular field be 'L'
and width be 'B'
Therefore, the fence required = 2B + L
Total cost of fence, C = $40L + $10 × 2B = $40L + $20B ............(1)
Area of the field = 57,800 square feet
also, area of the field = B × L = 57,800
or
L =
substituting L in (1)
C =
for minimizing the cost
==0
or
0=
or
or
or
B = 340 feet
Length = =
or
Length, L = 170
Hence, to minimize the cost the dimensions should be 340 feet on sides and 170 on the opposite side of the bank