Opentop box form problem
Description
HP15C Owner's Handbook  Pages 189190
Exercise:
Using a rectangular piece of sheet metal 4 decimeters by 8 decimeters, an opentop box having a volume of 7.5 cubic decimeters is to be formed. How should the metal be folded? (A taller box is preferred to a shorter one.)
Solution:
You need to find the height of the box (that is, the amount to be folded up along each of the four sides) that gives the specified volume. If x is the height (or amount folded up), the length of the box is (8 – 2x) and the width is (4 – 2x). The volume V is given by
V = (8 – 2x)(4 – 2x)x
.
By expanding the expression and then using Horner's method (page 79), this equation can be rewritten as
V = 4 ((x – 6)x + 8)x
.
To get V=7.5, find the values of x for which
f(x) = 4((x – 6)x + 8)x – 7.5 = 0
.
Program Resources
Labels
Program
Line 
Display 
Key Sequence 

000 



001 
42,21, 3 
f LBL 3 

002 
6 
6 

003 
30 
− 

004 
20 
× 

005 
8 
8 

006 
40 
+ 

007 
20 
× 

008 
4 
4 

009 
20 
× 

010 
7 
7 

011 
48 
. 

012 
5 
5 

013 
30 
− 

014 
43 32 
g RTN 
