Question: 8 . Solve the following goal programming model graphically and by using the computer: [ begin { array } { l }

8. Solve the following goal programming model graphically and by using the computer: \[\begin{array}{l}\text { minimize } P_{1} d_{1}+P_{1} d_{1}^{+}, P_{2} d_{2}, P_{3} d_{3},3 P_{4} d_{2}^{+}+5 P_{4} d_{3}^{+}\\\text {subject to }\\\qquad \begin{aligned} x_{1}+x_{2}+d_{1}^{-}-d_{1}^{+} & =800\\5 x_{1}+d_{2}^{-}-d_{2}^{+} & =2,500\\3 x_{2}+d_{3}-d_{3}^{+} & =1,400\\ x_{j}, d_{i}^{-}, d_{i}^{+} & \geq 0\end{aligned}\end{array}\]

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