[MOVED] region of a system: picking point in region

[Navyguy]

Select the point which is in the feasible region of the system of inequalities.

. . .2x + 3y < 8
. . .5x + 2y < 7
. . .x > 0
. . .y > 0

. . .a. (1, 2)
. . .b. (1, 1)
. . .c. (0, 3)
. . .d. (3, 2)

My answer, after using Excel and a TI-84 calculator, is (3,2) from the list of possible answers. Thanks for looking over my answer.

 

[soroban]

Hello, Navyguy!

Select the point which is in the feasible region of the system of inequalities.

$\displaystyle \;\;2x\,+\,3y\:\leq\:8,\;\;5x\,+\,2y\:\leq\:7,\;\;x\:\geq\:0,\;\;y\:\geq\:0$

$\displaystyle a.\;(1,\,2)\;\;\;b.\;(1,\;1)\;\;\;c.\;(0,\,3)\;\;\;d.\;(3,\,2)$

Hey, come on! . . . You need a calculator/computer to answer this one ??


Does $\displaystyle a)\;(1,2)$ satisfy the inequalities?
It says: $\displaystyle x\,=\,1,\;y\,=\,2$ . . . plug them in!

$\displaystyle \;\;2(1)\,+\,3(2)\:\leq\:8$ . . . Is this true?
$\displaystyle \;\;$ We have: $\displaystyle \,2\,+\,6\:\leq\:8$ . . . yes

$\displaystyle \;\;5(2)\,+\,2(1)\:\leq\:7$ . . . Is this true?
$\displaystyle \;\;$We have: $\displaystyle \,10\,+\,2\:\leq\:7$ . . . NO!

Therefore, $\displaystyle a)\;(1,2)$ is not in the region.


Now test the other three points . . .

 

[Navyguy]

This is hard for some

Yes I'm trying to hard I think, This is hard for some and easy for others. Thanks for showing me ths easy way of putting the problem together. This is what I needed. thanks again.