Suppose a, b, c are nonnegative numbers, and 3a + 2b + c = 5, 2a + b − 3c = 1. Find the Maximum value of S = 3a + b − 7c.

Answer 1

Do you know linear programming?
draw 3 axis graph (x,y,z) is (a, b , c)
Find all the corners of (a,b,c)
when a = 0
(0,0,5) (0,5/2,0)
and
(0 , 0 , -1/3) (0 1, 0)

when b = 0
(0,0,5) ( 5/3,0,0)
and
(1/2,0,0) (0,0,-1/3) note negative

when c = 0
(0,5/2,0) ( 5/3,0,0)
and
(0,1,0) (1/2,0,0)

You have three likely corners
p (5/3, 0, 0)
q (0, 5/2, 0)
r (0, 0, 5 )
try
p
S = 5
try q
S = 5/2
try r
S = negative
so the biggest I got was 5