The Lofton Company Has Developed the Following Linear Programming Problem $\operatorname { Max } \quad x _ { 1 } + x _ { 2 }$

question 42

Essay

The Lofton Company has developed the following linear programming problem $\operatorname { Max } \quad x _ { 1 } + x _ { 2 }$
$\begin{array} { l l } \text { s.t. } \quad & 2 x _ { 1 } + x _ { 2 } \leq 10 \\& 2 x _ { 1 } + 3 x _ { 2 } \leq 24 \\& 3 x _ { 1 } + 4 x _ { 2 } \geq 36\end{array}$ but finds it is infeasible. In revision, Lofton drops the original objective and establishes the three goals
Goal 1:
Don't exceed 10 in constraint 1.
Goal 2:
Don't fall short of 36 in constraint 3.
Goal 3:
Don't exceed 24 in constraint 2.
Give the goal programming model and solve it graphically.

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