Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A simple example : $Z=3x_1 + 2x_2$

Z is a constant with no given value.

  • $x_1, x_2 >0 $
  • $ x_1 \leq 5$
  • $ x_2 \leq 8$

The lecturer said that the slope is $-3/2$ , which I understand. However, he stated that all lines possible using that equation are parallel to the line passing through $(0,3)$ and $(2,0)$ . I want to know how did he deduce that assumption ? I tried giving $x_1$ and $x_2$ a value of zero and solve, however $Z$ has no given value. How did he know that the line would pass through $(0,3)$ and $(2,0)$ ?

share|improve this question
    
Lines are parallel if they have the same slope. –  Alfonso Fernandez Dec 29 '12 at 14:28
    
Yes exactly, but how do you plot them when Z is not given ? –  NLed Dec 29 '12 at 14:29
    
You can't, but you can plot a parallel line if you pick $Z$ (or a point, that's equivalent). –  Alfonso Fernandez Dec 29 '12 at 14:30
    
Thank you for the info –  NLed Dec 29 '12 at 14:34
add comment

1 Answer

up vote 1 down vote accepted

He simply picked one of the infinitely many lines of slope $-3/2$: they’re all parallel to one another, so they’re all parallel to any one of them. He could just as well have picked the line through $(0,6)$ and $(4,0)$: every line of slope $-3/2$ is also parallel to that line.

He chose that specific line by setting $Z=6$: the equation is then $3x_1+2x_2=6$, so when $x_1=0$ we have $x_2=3$, and when $x_2=0$ we have $x_1=2$. He probably chose $6$ because it’s the product of the coefficients $2$ and $3$: in general the line $ax_1+bx_2=ab$ passes through the points $(b,0)$ and $(0,a)$, so the intercepts are exceptionally easy to locate.

share|improve this answer
    
Perfect that makes sense. And thanks for the tip regarding why he chose 6. –  NLed Dec 29 '12 at 14:33
    
@NLed: You’re welcome. –  Brian M. Scott Dec 29 '12 at 14:34
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.