1. BUS-221 Quantitative Methods
LECTURE 9

2. Learning Outcome
Knowledge - Be familiar with basic mathematical techniques including: linear programming, systems of linear equations, calculus (differential and integral)
Communication - Present analyses of business situations from a quantitative point of view. The analysis will demonstrate clarity of expression, use of terminology, knowledge of format, aptness for the user group
Contribution - Plan and manage their learning to ensure adherence to agreed submission dates and class discussion. Prepares homework assignments for in-class discussion.

3. Topics Review topics -Linear equations -Linear programming
-Optimisation
-Application

4. Average Value of a Function
Example 1 – Average Value of a Function

5. Differential Equations (1 of 3)

6. Summaries of Graphical Solution Methods
TABLE 7.4
ISOPROFIT METHOD
1. Graph all constraints and find the feasible region.
2. Select a specific profit (or cost) line and graph it to find the slope.
3. Move the objective function line in the direction of increasing profit (or decreasing cost) while maintaining the slope. The last point it touches in the feasible region is the optimal solution.
4. Find the values of the decision variables at this last point and compute the profit (or cost).
CORNER POINT METHOD
2. Find the corner points of the feasible reason.
3. Compute the profit (or cost) at each of the feasible corner points.
4. Select the corner point with the best value of the objective function found in Step 3. This is the optimal solution.
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7. Solving Flair Furniture’s LP Problem
Most organizations have access to software to solve big LP problems
There are differences between software implementations, the approach is basically the same
With experience with computerized LP algorithms, it is easy to adjust to minor changes
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8. Using QM for Windows Select the Linear Programming module
Specify the number of constraints (non-negativity is assumed)
Specify the number of decision variables
Specify whether the objective is to be maximized or minimized
For Flair Furniture there are two constraints, two decision variables, and the objective is to maximize profit
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9. Using QM for Windows
PROGRAM 7.1A – QM for Windows Linear Programming Computer Input Screen
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10. Using QM for Windows PROGRAM 7.1B – QM for Windows Data Input
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11. Using QM for Windows PROGRAM 7.1C – QM for Windows Output and Graph
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12. Using Excel’s Solver
The Solver tool in Excel can be used to find solutions to
LP problems
Integer programming problems
Noninteger programming problems
Solver is limited to 200 variables and, in some situations, 100 constraints
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13. Using Solver To use Solver, it is necessary to enter data and formulas
Recall the model for Flair Furniture is
Maximize profit = $70T + $50C
Subject to 4T + 3C ≤ 240
2T + 1C ≤ 100
To use Solver, it is necessary to enter data and formulas
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14. Using Solver Enter problem data
Variable names, coefficients for the objective function and constraints, RHS values for each constraint
Designate specific cells for the values of the decision variables
Write a formula to calculate the value of the objective function
Write a formula to compute the left-hand sides of each of the constraints
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15. Using Solver PROGRAM 7.2A – Excel Data Input
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16. Using Solver PROGRAM 7.2B – Formulas
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17. Using Solver PROGRAM 7.2C – Excel Spreadsheet
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18. Using Solver PROGRAM 7.2D – Starting Solver
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19. Using Solver PROGRAM 7.2E – Solver Parameters Dialog Box
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20. Using Solver PROGRAM 7.2F – Solver Add Constraint Dialog Box
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21. Using Solver PROGRAM 7.2G – Solver Results Dialog Box
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22. Using Solver PROGRAM 7.2H – Solution
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23. Using Excel QM PROGRAM 7.3A – Excel QM in Excel 2013
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24. Using Excel QM PROGRAM 7.3B – Excel QM Input Data
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25. Using Excel QM PROGRAM 7.3C – Excel QM Output
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