can someone show me how to do this calc 1 problem? i seriously have no idea

[skim milk]

it's a word problem, related rates where you find the function and differentiate it in order to maximize or minimize

heres the question:

A builder wishes to fence in 60,000 square meters of land in a rectangular shape. Because of security reasons the fence along the front part of the land will cost $2.00 per meter, while the fence for the other three sides will cost $1.00 per meter. How much of each type of fence will the builder have to buy in order to minimize the cost of the fence? What is the minimum cost?

 

[skim milk]

bump

any hints, direction, anything! please asap

 

[bleeb]

This is easy


just put it into an equation and then differentiate it.

 

[hdeck]

we did minimizing stuff in pre-cal =/

too bad that was 3 years ago

 

[FrogDog]

Originally posted by: hdeck
we did minimizing stuff in pre-cal =/

too bad that was 3 years ago

Indeed...I can't remember how to do these, it's been too long.

 

[bleeb]

Just make an equation for the cost of the fence.. then differentiate it to find the rate. once you find the rate where its minimum.. plug that back in to the first equation.

Alright so you have a rectangle... x and y (width, length)

And you know that x*y = 60,000 m^2

You know that one Y will cost 2.00/meter.
the other Y will cost 1.00/meter
X will cost 1.00/meter and since you have two, you have two * X @ 1.00/meter

Just create an equation using those constraints/parameters and then differentiate it. I believe you should solve for it using only 1 variable. find the minimum, then at that point, plug back into the equation and check your answer.

Good luck

 

[DrPizza]

let L be front (length) W=width

LW=60000
solve for either... L=60000/W

Cost = front + back + side + side
cost = 2L + L + W + W
cost = 3L +2W

Now, substitute for L (or W) to have only one variable.....
Differentiate, set = 0, solve.

 

[skim milk]

Originally posted by: DrPizza
let L be front (length) W=width

LW=60000
solve for either... L=60000/W

Cost = front + back + side + side
cost = 2L + L + W + W
cost = 3L +2W

Now, substitute for L (or W) to have only one variable.....
Differentiate, set = 0, solve.

after i tried to differentiate, i get some number = 0

it's neither L or W equals zero...... so how do i know which one to plug in for?

unless i'm differentiating wrong.....

help?

 

[SuepaFly]

I feel like since it asks for a minimum you'll need a parabolic function, so it has to have some sort of x^2 type function. Let me work on it a minute, will get back to you.

 

[dighn]

Originally posted by: fritolays

Originally posted by: DrPizza
let L be front (length) W=width

LW=60000
solve for either... L=60000/W

Cost = front + back + side + side
cost = 2L + L + W + W
cost = 3L +2W

Now, substitute for L (or W) to have only one variable.....
Differentiate, set = 0, solve.

after i tried to differentiate, i get some number = 0

it's neither L or W equals zero...... so how do i know which one to plug in for?

unless i'm differentiating wrong.....

help?

you need another equation so that you have only one variable after substitution

hint: has to do with area

 

[skim milk]

Originally posted by: dighn

Originally posted by: fritolays

Originally posted by: DrPizza
let L be front (length) W=width

LW=60000
solve for either... L=60000/W

Cost = front + back + side + side
cost = 2L + L + W + W
cost = 3L +2W

Now, substitute for L (or W) to have only one variable.....
Differentiate, set = 0, solve.

after i tried to differentiate, i get some number = 0

it's neither L or W equals zero...... so how do i know which one to plug in for?

unless i'm differentiating wrong.....

help?

you need another equation so that you have only one variable after substitution

hint: has to do with area

are you talking about L = 60,000/w

i already plugged it into the 3L + 2W equation

and differentiated

but i get a number = 0 instead of some variable = to some number

i hope you get what im saying, lol

 

[skim milk]

bump

this problem is irritating the hell out of me... omg

someone please lead me in the right direction!

 

[Eli]

*sob*..

I wish I was good at math.. 🙁 Math makes my brain lock up.. and I get very frustrated and can't think...

 

[dighn]

err i dunno what u could be doing wrong there so here it is

cost = 3L +2W
L = 60k/W

C = 180k/W + 2W
dC/dW = -180k/W^2 + 2 = 0
-180k + 2W^2 = 0
W^2 - 90000 = 0
W = +-300 disgard -

 

[SuepaFly]

the answer is:
W = 300m
L = 200m

Think of it this way... if you are going to guess and check, what would you need to do.
1. You would guess the W first.
2. With regards to W, you would figure out L (L=90,000m/W)
3. Now you want to plug in for a formula that will caclulate cost: 2W+2L+1L (the extra length is because one side costs twice as much)
4. Plug in what you figured L to be (90,000/W)
5. 2W +3(90,000/W)
6. Set equal to zero and solve.

If you do really want to check, try W=301 and W=299, both are equal in cost (1,200.0X vs 1,200even)