Convert LP constraints to equalities with slack‚ surplus‚ and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex tableau. 4. Recognize special cases such as infeasibility‚ unboundedness and degeneracy. 5. Use the simplex tables to conduct sensitivity analysis. 6. Construct the dual problem from the primal problem. CHAPTER OUTLINE M7.1 M7.2 M7.3 M7.4 M7.5 M7.6 M7.7 Introduction How to Set Up the Initial
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Problem 2.22: a. Formulate an LP model for this problem X1 = quantity of ornate‚ decorative wood frame doors produced X2 = quantity of windows produced Max Total Profit: 500X1+400X2 X1+0.5*X2≤40 0.5*X1+0.75*X2≤40 0.5 X1+X2≤60 X1‚ X2≥0 b. Sketch the feasible region Please refer to the graph below c. What is the optimal solution After calculations using solver in excel‚ we figure out that the max total profit available is $26‚000.00‚ when produce a mix of 20 units of doors and 40 units of windows
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Julia’s Food Booth Case Problem MAT 540- Quantitative Methods February 23‚ 2013 (A) Formulate and solve an L.P. model for this case. The following variables were be used: X1 = Slices of Pizza X2 = Hot Dogs X3 = BBQ Sandwiches The objective is to maximize profit. maximize Z= 0 .75X1+1.05X2+1.35X3 Subject to: 0.75X1+1.05X2+1.35X3≤1‚500 (Budget) 24X1+16X2+25X3≤55‚296in2 (Oven Space) X1≥X2+X3 X2X3≥2.0 X1‚ X2‚ X3≥0 (B) Evaluate the prospect of borrowing money before the first
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Teaching Suggestion 8.1: Importance of Formulating Large LP Problems. Since computers are used to solve virtually all business LP problems‚ the most important thing a student can do is to get experience in formulating a wide variety of problems. This chapter provides such a variety. Teaching Suggestion 8.2: Note on Production Scheduling Problems. The Greenberg Motor example in this chapter is largest large problem in terms of the number of constraints‚ so it provides a good practice
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Mikela Sammy U62 Caribbean Studies QUESTION: Access the measures that Caribbean countries could realistically undertake to minimize the danger posed by earthquakes. An earthquake is a sudden and violent shaking of the ground‚ sometimes causing great destruction‚ as a result of movements within the earth’s crust or volcanic action. This happens when two blocks of the earth suddenly slip past one another. The Earth’s crust is made up of about a dozen plates on which the continents and oceans
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GEORGE‚ S T –SHIRTS The case about George’s T-shirts can be studied or analyzed by grouping the material into eight different categories. Introduction ● George Lassiter‚ a project engineer for a major defense contractor and also an entrepreneur who manufactures and designs special events T-shirts ● He has owned this lucrative T-shirt business for six years ● Designed T-shirts for “special events” such as rock concerts‚ major sporting events‚ and special fund-raising events. ●
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to an integer linear programming problem. Answer Selected Answer: False Correct Answer: False . Question 3 2 out of 2 points If we are solving a 0-1 integer programming problem‚ the constraint x1 ≤ x2 is a conditional constraint. Answer Selected Answer: True Correct Answer: True . Question 4 .2 out of 2 points If we are solving a 0-1 integer programming problem with three decision variables‚ the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive
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business decision making (4th ed.). Hoboken‚ NJ: John Wiley & Sons. Vietz‚ Osmond. Weaknesses in an Internal Audit Control System. (2012).http://www.smallbusiness.chron.com/weaknesses-internal-audit-control-system-3810.html Williams‚ J. R.‚ Haka‚ S. F.‚ & Bettner‚ M. S. (2005). Financial & managerial accounting: The basis for business decisions (13th ed.). New York‚ NY: McGraw-Hill Companies.
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this problem. Decision Variable X1 = Generator X2 = Alternator Obj. = Maximum Profit X1 | X2 | Time | Activity | 2 | 3 | 260 | Wiring | 1 | 2 | 140 | Testing | Max. Profit = 250X1 + 150X2 Subject to: 2x1 + 3x2 < 260 X1 + 2x2 < 140 X‚y > 0 2x1 = 3x2 < 260 X1 =0 x2 = 0 2(0) = 3x2 = 260 2x1 = 3(0) =260 3x2 = 260 2x1 = 260 X2 = 86.7 x1 = 130 X1 + 2x2 = 140 X1 = 0
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456 MATHEMATICAL MODELING AND APPLICATIONS Homework 1 1. [15 points] Consider the following linear programming problem: Min z = 3x12x23x3 Subject to x1+2x2 +x3 14 x1+2x2+4x3 12 x1 x2 +x3 = 2 x3 3 x1; x2 unrestricted (a) [6 points] Reformulate the problem so it is in standard format. (b) [6 points] Reformulate the problem so it is in canonical format. (c) [3 points] Convert the problem into a maximization problem. 2. [20 points] A lathe is used to reduce the diameter of a steel shaft
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