final exam review Flashcards
What is the equation of a line and what do the variables represent?
y = mx + b
- y: Dependent variable (output)
- x: Independent variable (input)
- m: Slope (rate of change)
- b: Y-intercept (value of y when x=0)
What is the formula for the slope between two points and what do the variables represent?
m = (y2 - y1) / (x2 - x1)
- (x1, y1) and (x2, y2): two coordinates on the line
What is the future value (FV) formula for compound interest and what do the variables represent?
FV = PV (1+r)^n
- FV: future value
- PV: present value
- r: interest rate per period (decimal)
- n: number of periods
What is the present value (PV) formula and what do the variables represent?
PV = Fv / (1+r)^n
- PV: present value
- FV: future value
- r: interest rate period (decimal)
- n: number of periods
What is the formula for the future value (FV) of an ordinary annuity and what do the variables represent?
FV = PMT x ((1+r)^n-1 / r)
-PMT: Payment per period
- r: Interest rate per period (decimal)
- n: Number of periods
What is the formula for the present value (PV) of an ordinary annuity and what do the variables represent?
PV = PMT x (1-(1+r)^-n / r)
- PMT; payment per period
- r: interest rate per period (decimal)
- n: number of periods
What is the formula for loan payment (PMT) and what do the variables represent?
PMT = (PV)(r) / 1 - (1+r)^-n
- PV: Loan amount
- r: Monthly interest rate
- n: Total number of payments
What is the formula for future value (FV) with continuous compounding and what do the variables represent?
FV = PV x e^rt
- e: Euler’s number (≈2.718)
- t: Time in years
What is the regression line equation and what do the variables represent?
y = mx + b
- y: Dependent variable
- x: Independent variable
- m: Slope (rate of change)
- b: Intercept
What is the formula to calculate the slope (m) in regression analysis and what do the variables represent?
m = n∑xy - ∑x∑y / n∑x^2 - (∑x)^2
- n: Number of data points
- n: Number of data points
- ∑xy: Sum of the product of x and y
- ∑x: sum of x values
- ∑y: sum of y values
- ∑x^2: sum of squared x values
- (∑x)^2: sum of x values squared
What is the formula to calculate the intercept (b) in regression analysis and what do the variables represent?
b = ˉy - m ˉx
- ˉy: average of y values
- ˉx average of x values
What is the formula for Sum of Squared Errors (SSE) and what do the variables represent?
SSE = ∑(Yi - Yi^)^2
- Yi: actual value of y
- Yi^: predicted value of y
What is the formula for exponential smoothing and what do the variables represent?
Ft+1 = αYt + (1-α)Ft
- Ft+1: forecast for the next period
- Yt: actual value for the current period
- Ft: forecast for the current period
- α: smoothing constant (between 0 and 1)
What is the objective function in linear programming and what do the variables represent?
Z = c1x1 + c2x2
- Z: Quantity to maximize or minimize
- c1, c2: coefficients fo each variable
- x1, x2: decision variables
What is the formula for a constraint in linear programming and what do the variables represent?
a1x1 + a2x2 ≤ b
- a1, a2: resource use per unit of each variable
- b: maximum available resources
What is the formula for the graphical solution in linear programming?
- Plot each constraint as a line.
- Identify the feasible region where all constraints overlap.
- Evaluate the objective function at the corners of the feasible region to find the optimal solution.
What is the definition of shadow price in linear programming?
Shadow price measures how much the objective (Z) changes if a constraint limit (b) increases by one unit.
What is the definition of reduced cost in linear programming?
- If zero: The variable is part of the solution.
- If non-zero: The amount the objective coefficient must improve for the variable to enter the solution.
What are the steps for using Excel Solver in linear programming?
- Define the objective (maximize/minimize).
- Identify decision variables.
- Add constraints.
- Run Solver and interpret reports (Answer, Sensitivity, Limits).
