Calculus applied application problem. Listed below.

Question

anonymous · Answer

You are going to build a rectangular enclosure for a garden. You are using the wall of your garage as one boundary of the garden and are using fencing to create the other 3 sides. You are also going to divide the garden in half by putting up a fence perpendicular to the garage wall. What is the minimum amount of fencing you can use if the garden must enclosure 120 square feet?

campbell_st · Answer

ok.... so draw a diagram 

|dw:1386657056901:dw|

you know from the area information 

$$120 = 1 \times w$$

and you know the perimeter is 

$$P = 2w + l$$'

so take the area formula and make l the subject

$$l = \frac{120}{w}$$

and substitute it into the perimeter formula 

$$P = 2w + \frac{200}{w}$$

so the next thing to do is find the 1st derivative

then let it equal zero

$$\frac{dP}{dw} = 0$$

and solve for w

when you have the value, substitute it into the area fromula to find the length. 

then you'll be able to find the perimeter

hope this helps.

anonymous · Answer

ic, i did it where the garage wall is part of the width. does that work too?

campbell_st · Answer

still works the same.... 

you will end up with 2 numbers that multiply to the area.... 

you just need to clearly define which is which for when you find the perimeter

anonymous · Answer

i see, so i have a really quick question, i already did all the work but i just need you to say "yes thats how u do it" or "no, u can't do that" for this equation:

A standard soda can has a volume of 250cm^3 and the top is double-thicknesss so counts twice as surface area in finding the amount of metal used to make the can. Find the dimensions of the can with the minimum surface area. 

I've already solved and to find the necessary dimension, its basically telling them what the radius and height is right? And for the surface area, normally it would be 2pi r^2 +2pi rh but since i have a double thickness, then i just have to add another pir^2 to the equation right?

campbell_st · Answer

I'd expect so... odd question.... I've not seen it before....

anonymous · Answer

I see, our calculus teacher loves to create odd problems. But i was just scared if I was doing the whole "thing" correctly. Thanks for all your help! Greatly appreciated.

campbell_st · Answer

well you may like to ask your calculus teacher... what it would look like... or where in "real life" this would occur...