1. Solve the following problem graphically. max 2x + y (1)

s.t. 4x + y 12 (2)

2x + 3y 18 (3)

x + 2y 4 (4)

x 0 (5)

y 0 (6)

Hint: Recall, you should plot the feasible region, and draw objective contours to figure out which way the objective is increasing.

2. (a) Reformulate the problem with only equality constraints by adding new slack and surplus variables; 1

(b) Repeat question 3, but change the objective function to 3x + 1 5 y instead;

(c) Repeat question 3, but change the objective to min 2x + y instead.