Post on 21-Dec-2015
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
ProblemSolving
DecisionMaking
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.
xinchange
yinchangeslope
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
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+23 (y+2) + 2y = 163y + 6 + 2y = 165y = 16 - 6 = 10
y = 10/5 = 2 x = y + 2 = 2 + 2 = 4
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
Modeling for Decision-Making
Uncontrollable Inputs(Constraints, etc.)
Controllable Inputs(Decision Variables)
Mathematical ModelOutput
(Projected Results)
Break-even Analysis
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
QaP BQcK
Break-even Analysis
KP
BQcQa
BQca )(
)( ca
BQ
BQcQa
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
)( ca
BQ
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