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## Homework Statement

Formulate as a mixed integer programming problem but do not solve. Maximize ##x_1 + x_2## subject to ##2x_1 + 3x_2 \le 12## or {##3x_1 + 4x_2 \le 24## and ##-x_1 + x_2 \ge 1##} ##x_1, x_2 \ge 0##

## Homework Equations

## The Attempt at a Solution

if the first constraint is met, we have upper bounds ##x_1 = 6, x_2 = 4##,

so ##2x_1 + 3x_2 - 12 \le 2(6) + 3(4) -12 = 12##

if the set of constraints is met, from the first constraint of the set we have upper bounds ##x_1 = 8, x_2 = 6## and from the second constraint of the set we have upper bounds ##(-x_1 \ge 1) \rightarrow (x_1 \le -1) \rightarrow x_1 = 0?, x_2## is not bounded above.

Therefore, for the whole set, we have upper bounds ##x_1 = 0, x_2 = 6##

Therefore, ##3x_1 + 4x_2 - 24 \le 3(0) + 4(6) - 24 = 0##

and ##-x_1 + x_2 - 1 \ge -(0) +(0) - 1 = -1##

So the model is Maximize ##x_1 + x_2##

subject to

##2x_1 + 3x_2 - 12 \le 12(1 - y_1)##

##3x_1 + 4x_2 - 24 \le 0(1 - y_2)##

##-x_1 + x_2 -1 \ge -1(1 - y_2)##

##y \space \epsilon##{0,1} and ##x_i \ge 0## for all i.

the answer key has ##-x_1 + x_2 -1 \ge -7(1 - y_2)## instead of -1 in my third constraint... where did i go wrong?