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1. Consider the following linear programing program: Max Z Z = 5x1 + 4x2 s. t. 2x1 + 2x2 $ 120 3x1 + 2x2 $ 150 X1 $ 40 X1,X2 20 a) Solve graphically. b) Using the graphical solution, find the range of c1 for which the optimal solution stays the same? C) Solve the problem using the SIMPLEX method (algorithm). d) Using the final tableau in c) for what range of C2 will the current solution remain optimal? e) Using the final tableau in c) for what range of b, will the current product mix remain the same? f) Solve using SOLVER.2. A mining company desires to blend a new alloy of 40 percent tin, 35 percent zinc, and 25 percent lead from several available alloys having the following properties: Alloy 1 2 3 4 5 % of tin 60 25 45 20 50 % of zinc 10 15 45 50 40 % of lead 30 60 10 30 10 Profit ($/1b) 22 20 25 24 27 The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a maximum profit. Formulate a linear programming model for this problem.3. Consider the following LP: Max 31x1 + 35x2 + 32x3 s. t. 1) 3x1 + 5x2 + 2x3 2 90 2) 6x1 + 7x2 + 8x3 $ 150 3) 5x1 + 3x2 + 3x3 $ 120 X1, X2, X3 2 0 The following optimal solution and output are provided: Variable Value Reduced Cost X1 13.333 0.000 X2 10.000 0.000 X3 0.000 10.889 Constraint Slack/Surplus | Dual Price 1 0.000 -0.778 2 0.000 5.556 3 23.333 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 30.000 31.000 No Upper Limit X2 No Lower Limit 35.000 36.167 X3 No Lower Limit 32.000 42.889 Constraint Lower Limit Current Value Upper Limit 77.647 90.000 107.143 2 126.000 150.000 163.125 3 96.667 120.000 No Upper Limit a) Give the solution and value to the problem. b) Which constraints are binding? c) What would happen if the coefficient x1 increased by 3? d) What would happen if the right hand of constraint 1 increased by 10? e) Formulate the dual and provide its optimal solution and value