Mathematical modeling

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Figure 2.13: Marketing example showing the optimum solution2.4.3 Solving Using Solver ProgramThe problem formulation on Excel is shown in Fig. 2.14, while the Solver setting isshown in Fig. 2.15. The complete report of the problem solution is shown in Fig. 2.16.Figure 2.14: Problem <strong>modeling</strong> in ExcelFigure 2.15: Solver settingSystems Analysis 27 Dr. Emad Elbeltagi
Figure 2.16: Final solver report of the marketing problem2.5 Types of Linear Programming SolutionsWhenever a linear programming model is formulated and solved, the result will be one offour characteristic solution types: 1) unique optimal solution, 2) alternate optimalsolutions, 3) no-feasible solution, and 4) unbounded solutions. The following exampleillustrates these different situations.Illustrative exampleA small company produces construction materials for the commercial and residentialconstruction industry. The company produces two products: a universal concrete patchingproduct (CON) and a decorative brick mortar (MORT). The company can sell the CONfor a profit of LE 140/ton and the MORT for a profit of LE 160/ton. Each ton of the CONrequires 2 m 3 of the red clay and each ton produced of the MORT requires 4 m 3 . Amaximum of 28 m 3 of the red clay could be available every week. The machine used toblend these products can work only a maximum of 50 hours per week. This machineblends a ton of either product at a time, and the blending process requires 5 hours tocomplete. Each material must be stored in a separate curing vat, thus limiting the overallproduction volume of each product. The curing vats for CON and MORT have capacitiesof 8 and 6 tons, respectively. What is optimal production strategy for the company giventhis information?Systems Analysis 28 Dr. Emad Elbeltagi
Page 6: Assume: Z= value of overall measure
Page 9: By solving the previous two constra
Page 12 and 13: Changeable cells(variables)Target c
Page 14 and 15: 2.4 Second Example: Market Allocati
Page 18 and 19: Model formulationFirst we have to d
Page 20 and 21: 2.5.3 Problems Having No Feasible S
Page 22 and 23: These assumptions are quite restric
Page 24 and 25: 2.7.2 Workforce PlanningProblem Def
Page 26 and 27: Now, let's look at the average risk
Page 28 and 29: Profit produced from each 240-m 2 h
Page 30 and 31: Monthly delivery to wholesaler 2Mon
Page 32 and 33: solve the following problem using t
Page 34 and 35: espectively. If 100 units of raw ma
Page 36 and 37: In a given period there are 600 hou
Page 38 and 39: Minimize z = - 4x 1 - 6x 2Subject t

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