1

Part of 1966 Vietnam National Olympiad

Problems(1)

max of x + y + z, if (x +cy<=36),(2x+ 3z>= 72), x,y,z >=0

Source: Vietnamese MO (VMO) 1966

x, y

z

be nonnegative real numbers satisfying the following conditions: (1)

x + cy \le 36

2x+ 3z \le 72

c

is a given positive number. Prove that if

c \ge 3

then the maximum of the sum

x + y + z

36

c < 3

, the maximum of the sum is

24 + \frac{36}{c}

algebrainequalitiesmaximum valueminimum value