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

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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(32388) 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

The feasible region is then,

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.