SOLUTION: Which point gives the minimum value for P = 3x + 2y and lies within the system of restrictions? ( < all of them are equal or greater than but i just dont kno how to do that o

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: Which point gives the minimum value for P = 3x + 2y and lies within the system of restrictions? ( < all of them are equal or greater than but i just dont kno how to do that o      Log On


   

Question 176633: Which point gives the minimum value for P = 3x + 2y and lies within
the system of restrictions?

( < all of them are equal or greater than but i just dont kno how to do that on here)
1 < x < 6
2 < y < 5
x + y < 10

A. (1, 2) B. (0, 0) C. (5, 5) D. (1, 5)
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
First find the feasible region and vertices.
1+%3C=+x+%3C=+6
2+%3C=+y+%3C=+5
The last one involves a little more work.
x%2By%3C=10
y%3C=-x%2B10
Let's graph the line and the other boundaries
drawing%28+300%2C+300%2C+-1%2C+11%2C+-1%2C+11%2Cgrid%28+1+%29%2Ccircle%28+0%2C+0%2C+.2+%29%2C%0D%0Agreen%28line%28-2%2C2%2C12%2C2%29%29%2C%0D%0Agreen%28line%28-2%2C5%2C12%2C5%29%29%2C%0D%0Agreen%28line%281%2C-1%2C1%2C15%29%29%2C%0D%0Agreen%28line%286%2C-1%2C6%2C15%29%29%2C%0D%0Agraph%28+300%2C+300%2C+-1%2C+11%2C+-1%2C+11%2C+-x%2B10%29%29+
The feasible region is then,
drawing%28+300%2C+300%2C+-1%2C+7%2C+-1%2C+7%2Cgrid%28+1+%29%2C%0D%0Acircle%28+1%2C+2%2C+.2+%29%2C%0D%0Acircle%28+1%2C+5%2C+.2+%29%2C%0D%0Acircle%28+6%2C+2%2C+.2+%29%2C%0D%0Acircle%28+6%2C+4%2C+.2+%29%2C%0D%0Acircle%28+5%2C+5%2C+.2+%29%2C%0D%0A%0D%0Agreen%28line%281%2C2%2C6%2C2%29%29%2C%0D%0Agreen%28line%281%2C2%2C1%2C5%29%29%2C%0D%0Agreen%28line%285%2C5%2C6%2C4%29%29%2C%0D%0Agreen%28line%286%2C2%2C6%2C4%29%29%2C%0D%0Agreen%28line%286%2C4%2C5%2C5%29%29%2C%0D%0Agreen%28line%285%2C5%2C1%2C5%29%29%0D%0A%29+
The vertices are then
(1,2)
(1,5)
(6,2)
(6,4)
(5,5)
The corresponding values of P are
P%281%2C2%29=3%281%29+%2B+2%282%29=7
P%281%2C5%29=3%281%29+%2B+2%285%29=13
P%286%2C2%29=3%286%29+%2B+2%282%29=22
P%286%2C4%29=3%286%29+%2B+2%284%29=26
P%285%2C5%29=3%285%29+%2B+2%285%29=22
The minimum value for P of 7 occurs at (1,2).
The correct answer is A.