Consider the following linear programming problem: (i) Create the initial simplex tableau (ii) Using the simplex method, examine and solve the problem b) The following tableau represents a specific simplex iteration. Iteration Basic variable X1 X2 S1 S2 RHS Ratio 0 S1 S2 1 4 2 3 1 0 0 1 40 120 20 40 Z -40 -50 0 0 0 1 X2 S2 0.5 2.5 1 0 0.5 -1.5 0 1 20 60 40 24 Z -15 0 25 0 1000 2 X2 X1 0 1 1 0 0.8 -0.6 -0.2 0.4 8 24 Z 0 0 16 6 1360 Major Topic LP: Slack/Surplus Blooms Designation AN Score 5 Major Topic LP: Simplex Method Blooms Designation AN Score 7 4 (i) Analyzing the tableau, can we say the solution to this problem is optimal at iteration 1? Explain (ii) Categorize the variables as Basic and non-Basic, and provide the current values of all the Variables. (iii) In your identification of the basic and non-Basic variables, determine the associated leaving variable if each such variable enters the basic solution. Major Topic Simplex Method: Basic and Non-Basic variable Blooms Designation EV Score 7 c) Consider the following problem. (i) Construct the dual problem. (ii) Graph the dual problem Major Topic Duality Theory Blooms Designation EV Score 6 d) Explain why the utilization factor rho for the server in a single-server queueing system must equal 1-P0, where P0 is the probability of having 0 customers in the system Major To
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