Question

A cubical box is to be constructed from three kinds of building materials. The material used in the four sides of the box costs 2c/in^2, the material in the bottom costs 3c/in^2 and the material for the lid costs 4c/in^2. Estimate the additional total cost of all the building materials if the length of a side is increased from 20 in to 21 in.

How in the hell do you set up this linear approx problem

Answer 1

Can you re-phrase this
How in the hell do you set up this linear approx problem

Answer 2

As for the problem
A cubical box means equal length L for width, length and height. L in inches
Cost for the bottom is 3cL^2
top: 4cL^2
sides: 4 sides * 2cL^2= 8cL^2
add it up
15cL^2
now examine what happens when you change from L=20 to L=21

Answer 3

doesnt work but thanks for your help

Answer 4

What did you get?

Answer 5

The difference is 615 but I dont think thats what its asking. Its in the linear approx/ marginal cost of my book

Answer 6

How about this:
Cost(L) = 15L^2 c (btw, is c a constant or does it stand for some unit of money e.g.cents ?)

If we use a linear approximation:
\[C_{apprx}(\Delta L)= C(20)+\Delta \frac{d C(L)}{dL}|_{L=20}\]

The incremental cost is
dC/dL = 30L c, at L=20 this becomes 600 c

so maybe the (approximate) answer is 600

Answer 7

600 is correct... lol okay how did you get that??

Answer 8

like could you run me through as if you are just teaching me linear approximation because I do not understand any of what ouy just wrote lol

Answer 9

Do you know calculus?

Answer 10

yes but that just doesnt make sense to me. My book does horribly at teaching LA and my teacher didnt do any of what you jsut did.

Answer 11

OK. Let's say you have a function (formula if you like) that tells you the cost of x widgets.

for example, C(x)= x you can graph this