jmc

Question

Let x and y be real numbers such that 3x + 2y 7 and 2x + 4y 8. Find the largest possible value of x + y.

Accepted Answer

Dividing the second inequality by 2, we get

x + 2 y \leq 4.

Adding the first inequality

3 x + 2 y \leq 7,

we get

4 x + 4 y \leq 11,

so

x + y \leq \frac{11}{4} .

Equality occurs when

x = \frac{3}{2}

and

y = \frac{5}{4},

so the largest possible value of

x + y

is

\frac{11}{4} .