Thread: Optimization Problem

A rectangular garden is to be surrounded by a fence joined to a 3 m long wall on one side. The opposite side to the wall has a 1 m opening ( for a later gate). There is40 m of fencing available. To maximize the garden area, the length of fence to be added to the wall side is:

Thank you.

Originally Posted by Hakhengkim

A rectangular garden is to be surrounded by a fence joined to a 3 m long wall on one side. The opposite side to the wall has a 1 m opening ( for a later gate). There is40 m of fencing available. To maximize the garden area, the length of fence to be added to the wall side is:

Thank you.

let L = total length of the side with the wall

W = length of the side perpendicular to L

40 = (L - 3) + (L - 1) + 2W

22 = L + W

W = 22 - L

area, A = LW = L(22 - L)

shouldn't need calculus to find the value of L that maximizes the area.

remember that the question is asking for the value of (L - 3).