SOLUTION: A rectangular storage bin is to be made from a rectangular piece of sheet metal 16 in. by 14 ​in., by cutting out equal corners of side x and bending up the​ sides. Exp

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A rectangular storage bin is to be made from a rectangular piece of sheet metal 16 in. by 14 ​in., by cutting out equal corners of side x and bending up the​ sides. Exp      Log On


   

Question 1072574: A rectangular storage bin is to be made from a rectangular piece of sheet metal 16 in. by 14 ​in., by cutting out equal corners of side x and bending up the​ sides. Explain how to determine the maximum possible capacity for a storage bin constructed in this way. What is the maximum possible​ capacity?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
v is volume as a function of x; x is the length of corner square to remove.
v=%2816-2x%29%2814-2x%29x

Simplify v into general form through multiplications. Find dv%2Fdx, equate to 0 and look for local maximum.

v=224x-60x%5E2%2B4x%5E3

dv%2Fdx=224-120x%2B12x%5E2

Set to 0.
12x%5E2-120x%2B224=0
3x%5E2-30x%2B56=0
x=%2830%2B-+sqrt%28228%29%29%2F%282%2A3%29
x=%2830%2B-+12%2Asqrt%282%29%29%2F6

highlight_green%28x=5-2%2Asqrt%282%29%29, x to get maximum v