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.

Question

Kade Crane

Mathematics

10 April, 11:10

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.

+3

Answers (1)

Know the Answer?

Jensen Hester · 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