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

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

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?

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?

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 Problem Solving Decision Making Decision

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

Coordinate System (x, y)

Quadrants (x, y)

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

Graphing Linear Equations Example: x + 2y = 6

Examples Plot 2x - y = 8 Plot x = 2y - 10

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

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

y-Intercept Example: x + 2y = 6 y-intercept

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

Examples What is the equation for this line:

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

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

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

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

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

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

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

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

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?

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