Georgie has a large rectangular garden area with

dimensions l metres by w metres which she wishes to

divide into three sections so she can grow different

vegetables. She plans to put a watering system along

the perimeter of each section. This will require a

total of 120 metres of hosing.

a. Show the total area of the three sections, A m2 is

given by A = 60w − 2w2 and hence calculate the

dimensions when the total area is a maximum.

SumDudWhoIsBadAtMath May 23, 2021

#1**+1 **

It is necessary to make the assumption that the L length is cut into 3 so that the three gardens are all W wide.

The length of the 3 doesn't matter so long as the 3 add together to be L in length.

This is what it must be, the w sides are all parallel.

Now you can add up all the sides and put them equal to 120.

Then solve for L

and substitute A=WL to get the area given.

After that find dA/dW and put it equal to 0 to find the W that will make the Area maximum.

That should be enough to get you one your way.

Other answerers: **Please allow Sumdud to do it from here. **

If Sumdud needs more help he/she will show what they have done and ask for further assistance.

Melody May 23, 2021