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- 22) Determine using the Simplex algorithm the optimal solution to the following linear programming problem:Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader–client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows: Requireda. Develop a network representation of this problem.b. Find the optimal solution using the Hungarian method. What is the total time required?Part A: “Infeasibility means that no solution to the LPP satisfies all the constraints, including the non-negativity restrictions.” Discuss on the above statement.
- .A linear programming problem has objective function P = 3x+2y and the following linear inequality constraints below. How many slack variables are needed for the simplex algorithm? What is the correct way to arrange this equation in order to enter it into a Simplex Tableau?First 3 parts are solved. 5-28 Consider the linear programmax x1 + x2s.t. x1 + x2 ≤ 9-2x1 + x2 ≤ 0x1 - 2x2 ≤ 0x1, x2 ≥ 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the modelin standard form.(c) Apply rudimentary simplex Algorithm 5Ato compute an optimal solution to yourstandard form starting with all slacks basic.(d) Plot your progress in part (c) on thegraph of part (a).(e) How can the algorithm be making progress when l = 0 if some moves of part(c) left the solution unchanged? Explain.5-29 Do Exercise 5-28 for the LPmax x1s.t. 6x1 + 3x2 ≤ 1812x1 - 3x2 ≤ 0x1, x2 ≥ 0Consider the following linear programming problem: A. Identify the feasible region. B. Are any of the constraints redundant? If yes, then identify the constraint that is redundant.
- a) is your colleague correct in their assertion? if not, how would you explain to them why this tableau does not offer the optimal solution? b) if this tableau yields the optimal solution, what is it? if not, identify the next pivot element according to the simplex algorithmConsider the following standard form LP problem (attached image): Let us introduce the additional constraint x1 + x2 = 3. Form the auxiliary problem and solve it using the big-M method.Consider the following primal problem and its dual, which of the following is the optimal solution?
- In a binary model which schedules a fire crew, the modeler wishes to impose the restriction that if employee B is selected to work on the shift, neither employee D nor employee E can be selected. How is this constraint to be written? Question 14 options: xD + xE + xB = 1 xD + xE + 2xB < 2 xD + xE - 2xB < 1 xD + xE + 2xB < 1 xD + xE + xB > 1Verify that in the example to the right, the same result isobtained if the constraint x + y = 20 is used to eliminate x rather than y.In some problems, we want that certain pairs of vertices are directly connected with each other. Modify Prim’s algorithm in order to solve the minimum spanning tree problem with this additional constraint.