Example 1
• Range of Optimality for c1 The slope of the objective function line is -c1/c2. The slope of the first binding constraint, x1 + x2 = 8, is -1 and the slope of the second binding constraint, x1 + 3x2 = 19, is -2/3. Find the range of values for c1 (with c2 staying 7) such that the objective function line slope lies between that of the two binding constraints: -1 < -c1/7 < -2/3 Multiplying through by -7 (and reversing the inequalities): 14/3 < c1 < 7

Example 1
• Range of Optimality for c2 Find the range of values for c2 ( with c1 staying 5) such that the objective function line slope lies between that of the two binding constraints: -1 < -5/c2 < -2/3 Multiplying by -1: Inverting, Multiplying by 5: 1 > 5/c2 > 2/3 1 < 5 < c2/5 < 3/2 c2 < 15/2

Right-Hand Sides
• The improvement in the value of the optimal solution per unit increase in the right-hand side is called the dual price. • The range of feasibility is the range over which the dual price is applicable. • As the RHS increases, other constraints will become binding and limit the change in the value of the objective function.

Dual Price
• Graphically, a dual price is determined by adding +1 to the right hand side value in question and then resolving for the optimal solution in terms of the same two binding constraints. • The dual price is equal to the difference in the values of the objective functions between the new and original problems. • The dual price for a nonbinding constraint is 0. • A negative dual price indicates that the objective function...

...WHOLE FOODS Case Analysis
Pelin Taser
Whole Foods Case Analysis
Situational Analysis –
Strengths: High quality-price point Brand-Non union-Customer satisfaction /service-Growth/profit-Processess-Innovative-Differentiating factors-Management-Employee oriented-Internet creating organic foods educated customers.
Weaknesses: Dept-High inventory cost-Price point-Narrow Target customers Base-Declining net income-Fast expansion-Low cash reserves-lack of innovation-High staff costs-High health care for employees-Limited add and marketing-Wild acquisitions –Unionization-Lower market share-commodity
Opportunities: International expansion-Increasing demand for products-Becoming and staying as top leading organic producer-Expanding private label-partner with new customer portals-Consumers against big box stores- Partner with new customer portals.
Threats: Competition-Stability and recession- Sameness experience-Diseases tied to organics- Became too big and fancy for customers-No more stores to acquire chains-food recall-contamination-Lower ad budget-
.
Problem Statement ––
Whole Food faces new treat of competition and the challenge of an outdated growth model.
Critical Issues –
(Segmentation strategy) Target audience for Whole foods?
Price sensitive or Health sensitive, Quality ,Selection
A) Cost of inventory
B) Out leveraged by competitions buying power
C) Competition is increasing
Alternative Solutions...

...Sensitivityanalysis, what-if analysis, and goal seeking analysis are used for same purpose to analyze complex relationships among millions of data items
to discover business patterns, trends.
All of them are part of Decision support systems (DSS) analysis techniques.
It helps managers to explore possible alternatives.
What-If Analysis:
In what-if analysis, an end user makes changes to variables, or relationships among variables, and observes the resulting changes in the values of other variables. Managers repeat this analysis with different variables until they understand all the effects of various situations. It differs from Sensitivty Analysis where manager changes only one variable at 1 time. It is changing an input value in an ad hoc way and seeing the result. Managers will not understand
assumptions of sensitivityanalysis and can't thoroughly explore solutions.
Example:
What happens if business cut marketing cost by 15%?
What happens if flood comes to New York city?
Sensitivty Analysis: -
Is a special case of what-if analysis. Typically, the value of only one variable is changed repeatedly, and the resulting changes on other variables are observed. So sensitivityanalysis is really a case of what-if analysis...

...SENSITIVITYANALYSIS
The solution obtained by simplex or graphical method of LP is based on deterministic assumptions i.e. we assume complete certainty in the data and the relationships of a problem namely prices are fixed, resources known, time needed to produce a unit exactly etc. However in the real world, conditions are seldom static i.e. they are dynamic. How can such discrepancy be handled? For example if a firm realizes that profit per unit is not Rs 5 as estimated but instead closer to Rs 5.5, how will the final solution mix and total profit change? If additional resources, such as 10 labor hours or 3 hours of machine time, should become available, will this change the problem's answer? Such analyses are used to examine the effects of changes in these three areas:
1. Contribution rates for each variable C FACTOR
2. Technological coefficients A FACTOR
3. Available Resources B FACTOR
This task is alternatively called sensitivityanalysis. It is also called as post optimality analysis.
Sensitivityanalysis often involves a series of what if? questions. What if the profit of product 1 increases by 10%? What if less money is available in advertising budget constraints? What if new technology will allow a product to be wired in one-third the time it used to take? So we can see that sensitivityanalysis can be...

...Sensitivityanalysis is a technique that indicates exactly how much a project's profitability (NPV or IRR) will change in response to a given change in a single input variable, other things held constant. Sensitivityanalysis begins with a base case developed using expected values (in the statistical sense) for all uncertain variables. Then, each uncertain variable is usually changed by a fixed percentage amount above and below its expected value, holding all other variables constant at their expected values. Thus, all input variables except one are held at their base case values. The resulting NPVs (or IRRs) are recorded and plotted.
Although sensitivityanalysis is widely used in project risk analysis, it does have severe limitations. If an input variable is not expected to vary much (is relatively certain), a project would not be very risky even if a sensitivityanalysis showed NPV to be highly sensitive to changes in that variable. In general, a project's stand-alone risk, which is what is being measured by sensitivityanalysis, depends on both the sensitivity of its profitability to changes in key input variables as well as the ranges of likely values of these variables. Because sensitivityanalysis considers only the first factor, it can give misleading results....

...Programming Notes VII
SensitivityAnalysis
1
Introduction
When you use a mathematical model to describe reality you must make approximations. The world is more complicated than the kinds of optimization
problems that we are able to solve. Linearity assumptions usually are signiﬁcant
approximations. Another important approximation comes because you cannot
be sure of the data that you put into the model. Your knowledge of the relevant
technology may be imprecise, forcing you to approximate values in A, b, or c.
Moreover, information may change. Sensitivityanalysis is a systematic study
of how sensitive (duh) solutions are to (small) changes in the data. The basic
idea is to be able to give answers to questions of the form:
1. If the objective function changes, how does the solution change?
2. If resources available change, how does the solution change?
3. If a constraint is added to the problem, how does the solution change?
One approach to these questions is to solve lots of linear programming problems.
For example, if you think that the price of your primary output will be between
$100 and $120 per unit, you can solve twenty di↵erent problems (one for each
whole number between $100 and $120).1 This method would work, but it is
inelegant and (for large problems) would involve a large amount of computation
time. (In fact, the computation time is cheap, and computing solutions to
similar...

...
SensitivityAnalysis
HCS/405
September 29, 2014
SensitivityAnalysis
Patton Fuller Community Hospital has been operating since 1975. Besides operating with the goal of keeping patient care their top priority there are other elements that demand the facility’s operations attention. At Patton Fuller Community Hospital there are elements that effect staffing, trend analysis and how that collected data is used forth going, how obtaining comparative data leads to forecasting, the type of plan taken for proper staffing at a hospital, and how a sensitive topic such as raises in wages and change can affect the staff, i.e. nurse-to-patient ratio.
Elements That Affect Staffing at Patton-Fuller
The elements that affect the health care staffing as observed at Patton-Fuller which includes raises in wages, the nurse-to-patient ratio changes, the contracted staff reduction, and the additional staffing of more nurses aides. By using trend analysis, the members of management of Patton-Fuller determine the type and amount of employees needed for medical facility staffing in order to maintain or improve operations above the level of quality. Using trend analysis will make us find out the costs that are associated with lessening the ratio of nurse-to-patient and this change's impact will be discussed as well. Planning, making decisions on whom to hire, and controlling are a few of the...

...Assignment #3 BLAW 502 (Summer Class I, 2013): The Richard Spellman Case
Total word count: 1724
1) Is there any need for Spellman to wade through the draft documents?
(224 words)
There is definitely the need for Richard Spellman to go through the draft documents. He needs to ensure that the employment deal that he had discussed with Walt Sawyer was in fact what the contract spelled out and that all information that has been exchanged informally, has been taken into consideration on the formal agreement.. In the “Open Items” email sent by Spellman to Sawyer, the only topic that wasn’t explained in further detail was Spellman’s base salary; further in-detail clarification was provided for bonuses, equity, and equity pool. Spellman stated that he was going to have his own lawyer read over the draft documents, but even with that precaution and the clarified points in the return email from Sawyer, he still needs to go over it himself to make sure nothing has been missed. The main reason he needs to do this is to make sure that he understands all aspects of all of the documents, including the restricted stock agreement, the consent of spouse, and arguably most important the employment agreement. If there are any issues in the documents that Spellman doesn’t understand or agree with, wants more clarification, etc., he will need to address them to his lawyer. His lawyer will then be better prepared to discuss any open items or questions with Peter Stone, Sawyer’s lawyer on...