Question

I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. If I have a budget of $80 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.]

… ft(smaller value) x … ft (larger value)
… ft2

Answer 1

have you made up an equation using the 80, and 2 and 4 dollars yet?

Answer 2

I did 4x+4y=80

Answer 3

Is that right?

Answer 4

yep, good.
now we need an equation for area..

Answer 5

Would it just be the equation of a regular rectangle?

Answer 6

A = wh ?

Answer 7

yep,
so with this question we want to maximize the area, so that means we will want w and h to be the same value

Answer 8

so going back to this equation:
4x+4y=80
we want x and y to be the same value, to maximize area with this particular problem, so we can do
x=y
thus
4x+4x=80
now solve for x

Answer 9

x=20-y ?

Answer 10

not quite...
we had 4x+4y=80
and to maximize the area of this problem, we want x and y to be equal lengths because they both have a 4 as a coefficient.
so we can say
y=x
so
this:
4x+4y=80
becomes
4x+4x=80
now just solve for x

Answer 11

x=10

Answer 12

so A = 100

Answer 13

Yay :) It's right!

Answer 14

Thank you! :) 2 more questions to go :p

Answer 15

yep ^_^
good job
just remember when ever your equation looks like ours did where x and y both had a 4 infront of them, then you have x=y