feasible region: x + 2y <= 10, 3x + y <= 10, ....

[Navyguy]

Which point is not a corner of the feasible region of a system of inequalities?

. . .x + 2y < 10
. . .3x + y < 10
. . .x > 0
. . .y > 0


. . .a. (10/3, 0)
. . .b. (2, 4)
. . .c. (0, 5)
. . .d. (10, 0)

My answer is (10/3,0) from a list of possible answers. After using Excel and a TI-84 calculator, I'm still not sure of my answer. Thanks for any help given.

 

[stapel]

Why are you not sure of your answer? You've graphed the four equations on your calculator and looked at which point(s) lie in the region, right? So what, specifically, is your question?

Thank you.

Eliz.

 

[soroban]

Hello, Navyguy!

Which point is not a corner of the feasible region of a system of inequalities?

\(\displaystyle \;\;x\,+\,2y\:\leq \:10,\;\;3x\,+\,y\:\leq\:10,\;\;x\:\geq\:0,\;\;y\:\geq\:0\)

\(\displaystyle \;\;a.\;\left(\frac{10}{3},0\right)\;\;\;b.\;(2, 4)\;\;\;c.\;(0, 5)\;\;\;d.\;(10, 0)\)

You don't know how to graph linear inequalities?

\(\displaystyle x\,\geq\,0,\;y\,\geq\,0\) places us in the first quadrant.


Graph the line: \(\displaystyle x\,+\,2y\:=\:10\)
It has intercepts \(\displaystyle (10,0)\) and \(\displaystyle (0,5)\).
Draw the line and shade the region below it.

Graph the line: \(\displaystyle 3x\,+\,y\:=\:10\)
It has intercepts \(\displaystyle \left(\frac{10}{3},0\right)\) and \(\displaystyle (0,10)\)
Draw the line and shade the region below it.

The region looks like this:

        |
      10*
        |*
        | *
       5o  *
        |:::o
        |::::*  o
        |:::::*     o
        |::::::*        o 
      - + - - - * - - - - - o -
        0      10/3         10

We can see three of the vertices: \(\displaystyle \,(0,0),\;(0,5),\;\left(\frac{10}{3},0)\)

The fourth vertex is the intersection of the two slanted lines.

Solve the system: \(\displaystyle \,\begin{array}{cc}x\,+\,2y\:=\:10 \\ 3x\,+\,y\:=\:10\end{array}\) . . . and get \(\displaystyle (2,4)\)

Got it?

 

[Navyguy]

thanks soroban

Thats what I needed to see, I think my ti-84 isn't set up right, I keep getting a window error. Thanks again soroban you are a big help while others are not.

 

[stapel]

Thanks again soroban you are a big help while others are not.

I apologize if you have been offended by most of the tutors asking what you had done and where you were having difficulty.

Eliz.