A store is going to construct a rectangular display area along one of the outsid

Question

A store is going to construct a rectangular display area along one of the outside walls of the store. There is 200 feet of fencing available to build it. The outside wall will provide a boundary for one side of the enclosure, so no fencing is needed there. Also, a 6-foot gate will be built into one side of the enclosure, so no fencing is needed there. Management wishes to construct the enclosure of maximum possible area. Let x denote the length, in feet, of the side of the enclosure that is opposite the wall of the store. Let y be the length, in feet, of one of the other two sides. Use the method of Lagrange Multipliers to solve, not other ways (very important).

1a- Write a system of equations that would need to be solved to determine the dimensions of the enclosure of maximum area. DECLARE ALL VARIABLES

1b- Determine the dimensions of the enclosure of maximum area

Explanation / Answer

a)

so L = x + 2y -6 = 200
where x is length oppsosite store wall and y is length perp to wall
L is length of frencing
A = x*y
A is area

b) langrange multiplier

f = xy - c ( x + 2y - 6 - 200)

df/dx = y - c = 0
y = c

df/dy = x - 2c = 0
x=2c

plug back into c0nstraint
2c + 2c - 6 = 200
4c = 206
c=51.5

so y = 51.5 and y = 103

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.