In preparing a ≥ constraint for an initial simplex tableau, you would a. add a surplus variable. b. add slack variable. c. subtract an artificial variable. d. subtract a surplus variable and add an artificial variable.
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- A. What is the optimal solution and what is the optimal value of the objective function? B. Which constraints are binding? C. What are the dual values? Interpret each. D. If you could change the right-hand side of one constraint by one unit, which one would you choose? Why?Which of the following is the converted constraint of 3x + 2y ≥ 35 under maximization of profit in simplex method? a. -3x +2y + S1 = -35 b. 3x +2y + S1 = 35 c. -3x -2y + S1 = -35 d. -3x -2y - S1 = -35 Which of the following is the converted constraint of 3x + 2y ≥ 35 under minimization of profit in simplex method? a. 3x + 2y - S1 + A1 = 35 b. 3x + 2y + S1 + A1 = 35 c. 3x + 2y + S1 - A1 = 35 d. 3x + 2y - S1 - A1 =-35 e. 3x + 2y - S1 + A1 =-351. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the above
- Indetify the constraints that form the fesible region and identify the constraints that are rebundant. Equation: Maximize 5x1 + 3x2 Subjected to x1 + 5x2 ≤ 5 4x1 + 3x2 ≤ 12 x1 + x2 ≤ 4 x1 + x2 ≤ 5 5x1 + 7x2 ≤ 35 x1 + x2 ≥ 0How will a change in the right-hand-side value for a constraint affect the optimalsolution?Find solution using BigM (penalty) method.Maximize Z = x1 + 2x2 + 3x3 - x4subject to the constraintsx1 + 2x2 + 3x3 = 152x1 + x2 + 5x3 = 20x1 + 2x2 + x3 + x4 = 10and x1, x2, x3, x4 ≥ 0
- Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?The manager of Jokitian Iron Works Company received an order to produce anumber of pipes which require the use of material A costing $3 and material Bcosting $8 per unit. For each pipe no more than 12 units of Material A and at least16 units of material B must be used. While each unit of A weighs 4 pounds andeach unit of B weighs 6 pounds, the final product must weigh exactly 120 pounds.a. Present the objective function.b. Present the constraint functions.c. Show and label the graph of the feasible solution.d. How many units of each raw material should be used in order to producethe ordered pipes most economically?e. What is the cost of each pipe?
- In problems involving maximization and minimization, what is the objective function? States intended outcome in equation form Incorporates constraint of maximum budget Lists set of potential restrictions on the solution Cites constraints to ensure objectivityConsider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Which of the following could not be a constraint for a linear programming problem? Multiple Choice 1A + 2B = 3 1A + 2B 1A + 2B ≤ 3 1A + 2B ≥ 3 1A + 2B + 3C ≤ 3