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. can someone help me solve this problem. Its in the marginal cost/linear approximation chapter of my calc book

Answer 1

Consider relating the cost of each portion (sides, top, bottom) of the box with the length of a side. Once you do that, you can see what changes happen when you increase the length of a side.

Answer 2

I tried making an equation by adding up all of the parts got 15L^2 tried doing that but it didnt really work, someoen else on here suggested that I use that equation.

Answer 3

let me see what I get:
cost of one side is 2L^2
top is 3L^2
bottom is 4L^2
Added and accounting for 4 sides does indeed give 15L^2.

Since we're doing calculus, when in doubt take a derivative! this gives us a "slope" of 30L, therefore, if you increase the length by 1, you get a cost increase of 30 cents.

Answer 4

Your equation (15L^2) gives a result of cents. By taking the derivative (in terms of length) you get a result in terms of cents per unit length, which is in the units you're looking for.

Answer 5

hmmm it says 30 is incorrect I tried that too

Answer 6

My calc teacher isnt doing units and he refuses to teach me the units way even in office hours. He literally thought us this for 20 minutes and said we were fine then we get ot the HW and none of us know hwo to do it lol

Answer 7

nothin on google either about how to do it

Answer 8

Well we can try to hardmode it. 15L^2 with L=20 give 15*400. 15L^2 with l=21 gives 15*441.
15*441-15*400 gives us 15*41 = 615.

I'm afraid that I must have missed something somewhere, if I can figure it out I'll be sure to let you know

Answer 9

i tried 615 too no dice :\, thank you!