MANSCIE-WEEK4

• Sensitivity analysis is a data-driven investigation of how certain variables impact a single, dependent variable and how much changes in those variables will change the dependent variable.
• There are many benefits of conducting a sensitivity analysis: 

  • This type of analysis allows for an assessment of change in all of the variables. 
  • If done correctly and highly detailed, the forecast can be more precise. 
  • It allows businesses to make knowledgeable decisions. 
  • It is very important for businesses to have the ability to understand how making a change, no matter how small it may seem, can potentially affect their profits and sensitivity analysis is another great tool that is easy to use and provides excellent value.
• Role of the Demand Equation in Sensitivity Analysis

  • The demand equation, or price elasticity of demand, is the mathematical representation of product price and quantity wanted. When using the demand equation in sensitivity analysis, it identifies how the change in demand is affected by a price change. 
  • The formula for the demand equation is the following: 

  PRICE ELASTICITY OF DEMAND = PERCENT CHANGE IN QUANTITY DEMAND / PERCENT CHANGE IN THE PRICE OF THAT SPECIFIC PRODUCT
• Graphical Solution Method is a two- dimensional geometric analysis of Linear Programming problems with two decision variables. The Theory of Linear Programming states that the optimal solution will lie at a corner point of the feasible region. In large Linear Programming problems, the feasible region cannot be easily graphs because it has many dimensions (hyperspace), but the concept is the same.
• Steps in Linear Programming Graphical Method

  1. Graph the linear inequalities and determine the feasible region. 

  2. Determine the coordinates of the extreme points (corner points). 

  3. Substitute the coordinates of the extreme points to the objective function and identify the highest (for maximization problem) or lowest (for minimization problem) result. 

  4. The highest (for maximization problem) or lowest (for minimization problem) result obtained in step 3 serves as the optimal solution to the LP problem.
• Simplex Method is an iterative technique that begins with a feasible solution that is not optimal, but serves as a starting point. With the use of algebraic manipulation, the solution is improved until no further improvement is possible. It is more convenient to solve linear programming models in simplex method with more two unknown variables because geometrically it is difficult to graph.
• Simplex Method


  A standard linear programming maximization model is required to maximize an objective function of the form
• Iteration


  A sequence of steps (row operations) performed in moving one basic feasible solution to another
• Simplex Tableau


  A table used to keep track of the calculations made when the simplex method is employed
• Right-Hand-Side (RHS)


  The column in a simplex tableau indicating the quantities of the variables in a solution
• Basic Variables (BV)


  Variables included in a basic solution
• Pivot column


  The column in any solution to a maximization problem which has the lowest negative value in the last row
• Intersectional Elements


  Elements common to both the pivot column and the rows representing variables in the solution
• Pivot Row


  The row in the simplex tableau corresponding to the basic variable that will leave the solution. It is determined by the test ratio and it is being computed by dividing the right-hand-side (RHS) by the intersectional elements (IE)
• Pivot


  The element of the simplex tableau that is in both the pivot row and the pivot column
• SENSITIVITY ANALYSIS AND INTERPRETATION OF RESULTS IN AN ACCOUNTING CONTEXT

  • Sensitivity Analysis shows how the CVP model will change with changes in any of its variables (e.g., changes in fixed costs, variable costs, sales, price, or sales mix). The focus is typically on how changes in variables will alter profit.