The dimensions required to minimize the cost of fencing is 180ft and 360 ft.
According to question
The cost of fence on opposite side of river is $40.
The cost of fence on other sides of river is $10.
Total yield = 64800 sq. feet
Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.
Area of fence = xy = 64800 sq feet
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Let C be the cost of making fence.
For cost to be minimum, dC/dx should be equal to zero.
C = 40x + 10y * 2
⇒ C =
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So, the dimensions needed will be 180 ft and 360 ft.
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