Optimization Problems

[Videoorchard]

Hi Tommy,

I have a question related to Optimization Problem on algebra strategy guide.

Question:
If -4<=m<=7 and -3<n<10, what is the maximum possible integer value for m-n?

My Question:
In the table presented at pg 90. how did you convert GT to LT? and vice versa.

i.e
(-4)-GT(-3)= LT (-1)
(-4)-LT10=GT(-14)


Question PG No:
Algebra Strategy guide.
Pg. 90

[n00bpron00bpron00b]

The LT/GT conversion gets quite confusing, here's how I tackle optimization problems -

-4 <= m <= 7
-3 < n < 10

Let's think in terms of the number line

The minimum value for M is -4
The maximum value for M is 7

The minimum value for N is -2.9
The maximum value for N is 9.9

Let's try few cases
M -> -4, 7
N -> -2.9, 9.9

1) -4 - (-2.9) = -1.1
2) -4 - 9.9 = -13.9
3) 7 - (-2.9) = 9.9 (M is greatest - N is least)
4) 7 - 9.9 = -2.9

Case 3 works - the max value of M-N could be 9.9 (but since we have been asked about "Integer" values)

The max value of M-N is 9

I suggest you to play around with those values :) you will eventually get the hang of it.

[tommywallach]

Yeah, I've answered this kind of question before. People are always looking for a RULE for optimization like this (i.e. "You switch GT to LT when blah blah blah..."). I don't recommend this, because it suggests a codified/hard approach. As I said with your other question, flexibility is key. Instead of trying to come up with a rule, test numbers along the boundaries of the range (as noob suggested). You'll VERY quickly see what's going on.

This is much safer than trying to have a built-in system.

Hope that helps!

-t

[Videoorchard]

Hi.

Greetings of the day!

Thank you for the explanation. The alternative method which you guys suggested (Making use of the actual boundary values) is perfect! Hmm. If making use of the boundary values is "much safer" or the better way, why did the author make use of the GT TO LT method anyway?

Although i will follow the approach which you recommended above, i am bit curious on HOW the author did the conversion of GT to LT (Or vice versa)...

Problem Piece:

1.

(-4)-GT(-3)= LT (-1)
(-4)-LT10=GT(-14)


2.

If -4<a<4 and -2<b<-1

Extreme value for a are GT(-4) and LT(4).
Extreme value for b are GT(-2) and LT(-1).

The most positive ab can be is GT(-4)xGT(-2)= GT(+8)
But the author writes it as
The most positive ab can be is GT(-4)xGT(-2)= LT(+8)


Problem Sources:

1.
Algebra Strategy guide.
Pg. 90

2.
Algebra Strategy guide.
Pg. 95

[Videoorchard]

To add to the fray, here's another problem involving GT to LT conversion.

4- 1.5xLT(-1) = 4 + GT (1.5) =GT (5.5)


I spent almost 4 hours pondering on this issue. Although i love the whole manhattan book experience,i am still wondering on why the author has not provided a detailed explaination on these type of conversion.

Source:
pg 160
Algebra strategy guide