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Quadradics -min/max problem help?

I have three questions left on my homework that I don't understand how to do. Can someone please explain to me how to work through these problems?

1. A rectangular field is to be enclosed by a fence and divided equally into 5 smaller plots by fences parallel to one of the sides. Determine the dimensions of the entire rectangular field if 1200m of fencing is used and the area must be a maximum.

2. Brookfield Trails operates a snowmobile lodge. Last year it had 100 guests whom each paid $160 per night. The manager estimates that she can expect 5 additional customers for each $1 reduction in price. Determine the cost of the room that produces the maximum revenue.

3. Algebraically determine the equation of the inverse for each of the following:
a)3y-4x+8=0
b)f(x)=¼(x-2)^2 -2

1. Lets say the dimensions are x and y and we will put fencing parallel to y
Then the total length of fencing can be expressed as 1200 = 6x + 2y or y = 600 – 3x

Now area can be written as A = xy

= x(600-3x)… substituting for y

Differentiate and equate to 0 to get max area

dA/dx = x(-3) + (600-3x)(1) = 0… using chain rule

3x = 600 – 3x

6x = 600, x = 100 and y = 600 – 3x = 600 – 300 = 300

Dimensions of field for max area are 100m by 300m and field is divided in 5 parts by fencing running parallel to the smaller side i.e. 100m

2. Let the rent be reduced by x dollars. Then, the total revenue can be expressed as R = (160 – x)(100 + 5x)

To maximize revenue, differentiate and equate to zero

dR/dx = (160-x)(5) + (100+5x)(-1) = 0

800-5x = 100+5x

10x = 700 or x = 70 and guests = 100+5x = 100+5*70 = 450

So the price can be reduced by $ 70 to make the rent $ 160-70=$90 and the total revenue will be

90 * 450 = $40,500

3. 3y – 4x + 8 = 0 or y = (4x-8)/3

inverse is x = (3y-8)/4 so f-1 = (3y-8)/4

y = ¼(x-2)2 – 2

sqrt(4(y+2)) = x-2

x = sqrt(4(y+2)) + 2 = sqrt(4y+8) +2

f-1 = sqrt(4y+8) +2

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