Lagrange Multipliers for Equality Constraints We purchased 180 yards of fence to enclose an area for planting sweet potatoes. Determine the dimensions of a rectangular area so that we can fence the maximum amount of area considering that one side of the rectangle does not need fence because of building.

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Mathematics

Reginald Potter

26 March, 00:12

Lagrange Multipliers for Equality Constraints We purchased 180 yards of fence to enclose an area for planting sweet potatoes. Determine the dimensions of a rectangular area so that we can fence the maximum amount of area considering that one side of the rectangle does not need fence because of building.

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Elijah Zavala · Answer 1

It would be good to know how wide the building is, but assuming 36 yards, the area could have a length of 72 yards and a width of 36 yards. The area enclosed would be 2592 square yards.

Step-by-step explanation:

x + 4x = 180

5x = 180

x = 36 one side width

2x = length of two sides = 72

Area = lw

72 x 36 = 2592