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###### 3. For the following linear programming (primal) problem Minimize Z -3x1 x2 - 2x3, subject to xx2...

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3. For the following linear programming (primal) problem Minimize Z -3x1 x2 - 2x3, subject to xx2 2x3 s 20 2xl x2 - x3 < 10 and xl20, x220, x32 0. (a) Find a standard form of the given problem and solve the problem using simplex (b) Find marginal costs corresponding each constraint of the primal (c) If we change the right hand side of the first constraint (10) to 10+A, then draw a graph representing the optimal value as a function of Δ when Δ changes. (d) Use algebraic analysis to find the allowable range to stay optimal for each cj.. (e) Use algebraic analysis to find the allowable range to stay reduced costs for each bi.

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