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

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subject to:

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

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

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$\\simplify{{c31} x + {c32} y <= {c3}}$

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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 triangle. Calculate objective function values at vertices and arrange them in assending order from smallest to largest as $f_1, f_2, f_3:$

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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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The optimal solution is: [[6]] = [[5]]

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$(x_{sol},y_{sol}) =$ ([[3]],[[4]])

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