PFA

PFA


SCHOOL OF QUANTITATIVE SECIENCES SQQM3024 MATHEMATICAL MODELING A211 QUIZ 1 PART 2 QUESTION ONE (12 Marks) Develop your own original LP problem with two constraints and two real variables. i. Explain the meaning of the numbers on the right-hand side of each of your constraints. ii. What is the criteria should you consider in deciding whether it would be easier to solve the problem by the corner point method or the isoprofit line method. iii. Solve your problem graphically to find the optimal solution. Interpret your solution. iv. Explain how a fifty percent (50%) increase in the objective function coefficient of your first variable (X1) over the value you originally assigned it affects your optimal solution. QUESTION TWO (12 Marks) Consider the following four LP formulations. Using the graphical approach, determine which formulation i. has a unique solution ii. is unbounded iii. has no feasible solution iv. has (alternative) or multiple optimal solutions (Note: Justify your answer) Formulation 1 Max 1 2X X Subject to 1 2 1 2 1 2 4 5 , 0 X X X X X X      Formulation 3 Max 1 24X X Subject to 1 2 1 2 1 2 8 2 16 5 2 12 , 0 X X X X X X      Formulation 2 Max 1 23X X  Subject to 1 2 1 2 1 2 4 2 4 , 0 X X X X X X      Formulation 4 Max 1 23X X Subject to 1 2 1 2 1 2 2 6 3 9 , 0 X X X X X X      QUESTION THREE (16 Marks) A manufacturing factory produces four products that consist of four operations: wiring, drilling, assembly, and inspection. The processing time in hours for each unit operation, its corresponding profit and the minimum monthly production level are given in TABLE 1. TABLE 2 shows the monthly available capacity for each operation. TABLE 1: Processing time per unit and profit OPERATION Profit (RM) Minimum production level Product Wiring Drilling Assembly Inspection 1 0.5 0.3 0.2 0.5 9 150 2 1.5 1 4 1 12 100 3 1.5 2 1 0.5 15 300 4 1 3 2 0.5 11 400 TABLE 2: Available capacity (hours) per month Operation Capacity (hours) Wiring 15000 Drilling 17000 Assembly 26000 Inspection 12000 i. Formulate an LP model for this problem. ii. Solve the problem using QM for Windows. Screenshot your answer. iii. From finding in (ii), would the solution change if the available capacity (hours) for wiring is changed from 15000 to 20000? iv. What is sensitivity analysis? From finding in (ii) explain how does sensitivity analysis works for objective function. v. From finding in (ii), discuss the dual (shadow prices) of a binding constraint.