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This question tests the student's ability to solve Linear Programming problems by applying Geometric method.

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Solve the following Linear Programming problem by applying the geometric method.

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Problem:

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Minimize:  \$\\simplify{{ox} x + {oy} y}\$

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subject to:

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\$\\simplify{-{c21} x - {c22} y <= -{c2}}\$

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\$\\simplify{-{c11} x - {c12} y <= -{c1}}\$

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\$x \\ge \\var{a1} \$

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\$x \\le \\var{a3} \$

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\$y \\le \\var{b2m} \$

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\$x \\ge 0\$

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\$y \\ge 0\$

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The feasible region in this problem is a pentagon with 5 corners. Calculate objective function values at corner points and arrange them in assending order from smallest to largest as \$f_1, f_2, f_3, f_4, f_5:\$

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\$f_1 =  \$ [[0]]

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\$f_2 = \$ [[1]]

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\$f_3 = \$ [[2]]

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\$f_4 = \$ [[3]]

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\$f_5 = \$ [[4]]

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The optimal solution is: [[8]] =  [[7]]

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\$(x_{sol},y_{sol}) =\$ ([[5]],[[6]])

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