Maximizing Area for 5 Lots with Side Restrictions

[Emethyst]

Homework Statement

A total length of 240m of fence is to be used to enclose and separate 5 retangular lots that are situated side-by-side.
a)Find the dimensions that yield the maximum area
b)Find the dimensions that yield the maximum area if each side of each lot nust be greater than 14m

Homework Equations

Implicit differentation

The Attempt at a Solution

I have solved a) and the only problem I am having is solving for b) (I included a) because I did not know if it may play a part in b)). What I do not know is where to use the 14m in the question. I thought it might be part of the domain, but this did not get me anywhere. If anyone could help me along here I would appreciate it greatly, thank you.

 

[lanedance]

hi Emethyst

this is an extra constraint on your solution

as you mentioned it constrains the solution such that width & height of each lot are >14m

this means the maximum could lie within the allowable domain (solution of first question) or on a boundary of the domain (where width or height = 14m). so your previously found maximum may no longer apply...

 

[Emethyst]

Thanks for the help lanedance, I just substituted it into the perimeter forumla and it worked great