Step-by-step explanation:
•x + y < 6
(6,6)
• 5x + y = 10
(2,10)
•x + 5y = 14
(14,14/5)
intersection I
x + 5y = 14
5x + y = 10
____________ •2
5x + 25y = 70
5x + y = 10
____________ _
24y = 60
y = 2 1/2 = 2,5
substitusion
5x + y = 10
5x + 2,5 = 10
5x = 7,5
x = 1,5
(1,5 , 2,5)
Intersection II
x + y = 6
5x + y = 10
_____________ _
-4x = -4
x = 1
x + y = 6
y = 6 - 1
y = 5
(1 , 5)
Intersection III
x + y = 6
x + 5y = 14
___________ _
-4y = -8
y = 2
x + y = 6
x = 6 - 2
x = 4
(4 , 2)
p = 10x + 26y
I.(1,5 , 2,5) = 10(1,5) + 26(2,5) = 15 + 65 = 80. (MINIMUM)
II.(1,5) = 10(1) + 26(5) = 10 + 130 = 140(MAXIMUM)
III.(4,2) = 10(4) + 26(2) = 40 + 52 = 92
SO,MINIMUM VALUE ------> 80
