INFM 718A / LBSC 705 Information For Decision Making

1. INFM 718A / LBSC 705 Information For Decision Making Lecture 1

2. Overview • Introduction • Aspects of decision making • Math refresher • Decision making process • Modeling for decision making • Break-even analysis

3. Questions • What information did you need to make the decision? • How did you define and compare the options? • Are you sure your choice is the best choice? • Are you sure your choice will stay the best choice? For how long?

4. Questions • What else would you like to have known before making the decision? • How did you feel while making the decision? • How did you feel after making the decision? • How do you feel now about your decision?

5. Decision-Making and Problem-Solving • Define the problem • Identify the alternatives • Determine the criteria • Evaluate the alternatives • Choose an alternative • Implement the decision • Evaluate the results Decision Making Problem Solving Decision

6. Math Refresher • Coordinate System, Quadrants • Graphing Linear Equations • Slope of a Line • Solving Linear Equation Systems • Graphing • Substituting • Addition

7. Coordinate System (x, y)

8. Quadrants (x, y)

9. Graphing Linear Equations • Example: x + 2y = 6 • Assign values to y and calculate x, based on the given y value. • y = 0  x = 6 (6, 0) • y = 1  x = 4 (4, 1) • y = 2  x = 2 (2, 2) • y = 3  x = 0 (0, 3) • Plot these points on the coordinate system

10. Graphing Linear Equations • Example: x + 2y = 6

11. Examples • Plot 2x - y = 8 • Plot x = 2y - 10

12. Slope of a Line • Pick two points, and find the changes in x and y. • Use the formula to calculate slope.

13. Slope of a Line • Example: x + 2y = 6 • Points: (6, 0) and (4, 1) • change in x = 6 - 4 = 2 • change in y = 0 - 1 = -1 • slope = -1/2 • y = mx + b y = -1/2 x + 3 slope y-intercept

14. y-Intercept • Example: x + 2y = 6 y-intercept

15. Examples • What is the slope of 2x - y = 8? • What is the y-intercept?

16. Examples • What is the equation for this line:

17. Solving Linear Equation Systems • Graphing • Substituting • Addition • Example: 3x + 2y = 16 x - y = 2

18. Graphing 3x + 2y = 16 Solution (4, 2) x - y = 2

19. Substituting 3x + 2y = 16 x - y = 2 x = y+2 3 (y+2) + 2y = 16 3y + 6 + 2y = 16 5y = 16 - 6 = 10 y = 10/5 = 2 x = y + 2 = 2 + 2 = 4

20. Addition 3x + 2y = 16 x - y = 2 (multiply by 2) 3x + 2y = 16 + 2x - 2y = 4 (add two lines) 5x = 20 x = 4 y = 2

21. Modeling for Decision-Making Uncontrollable Inputs (Constraints, etc.) Controllable Inputs (Decision Variables) Mathematical Model Output (Projected Results)

22. Break-even Analysis

23. Break-even Analysis • a: Revenue (income) per unit • B: Total fixed costs • c: Variable cost per unit • Q: number of units produced at BE point

24. Break-even Analysis • P: Total revenue at BE point • K: Total costs (fixed + variable) at BE point

25. Break-even Analysis

26. Break-even Analysis • a: Revenue (income) per unit • B: Total fixed costs • c: Variable cost per unit • Q: number of units produced at BE point

27. Goes Beyond Sales • Alex has determined that his car delivers 24 miles per gallon. With a $100 tune up, the car can deliver 30 miles per gallon. The price of gas is $3/gal. Assume the gas price steady, and the benefits of the tune up permanent. When will Alex reach break-even, driving at a rate of 20 miles per day?

28. Goes Beyond Sales • 4000 miles • 200 days • $.5 savings per day • $82.5 net savings at the end of year one • $182.5 savings per year thereon