SOLUTION: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of       Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 77542: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
a) Find the function V that represents the volume of the box in terms of x.

b) Graph this function and show the graph over the valid range of the variable x..

c) Using the graph, what is the value of x that will produce the maximum volume?


Answer by ankor@dixie-net.com(15652) About Me  (Show Source):
You can put this solution on YOUR website!
An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
:
The dimensions of the box will be (4-2x) by (6-2x) by x
:
a) Find the function V that represents the volume of the box in terms of x.
V = (4-2x)*(6-2x)*x
V = 4x^3 - 20x^2 + 24x
:
b) Graph this function and show the graph over the valid range of the variable x..
+graph%28+300%2C+200%2C+-1%2C+2%2C+-10%2C+20%2C+4x%5E3+-+20x%5E2+%2B+24x%29+
:
c) Using the graph, what is the value of x that will produce the maximum volume?
It is about .8 ft or about 9.6 inches.
Max vol would be 2.4 * 4.4 * .8 = 8.45 cu ft