Question

1.) Describe an application of linear programming that you might find useful where you work, in a course you are taking or in your personal life. Be specific with your answers. This is an opportunity for you to showcase what you have learned about linear programming and your ability to apply your knowledge to real-world applications. A comment such as "I do not use linear programming" will earn no credit. Do not write something general such as "I could use linear programming to maximize profits at work." If this is true, you do not have to formulate a mathematical model with numbers, but you should provide a general scenario and discuss possible constraints, controllable inputs, uncontrollable inputs, etc. (5 points)

2.) Explain why sensitivity analysis is an important part of modeling using linear programming. What is its purpose? This is an opportunity to showcase what you have learned about sensitivity analysis and your ability to apply your knowledge to linear programming. (5 points)

Answer 1

1) Let us consider the example of linear programming in the simple scenario where one statistics teacher want to coach his students online for which he choose three media of advertisement to attract his students namely 1) facebook 2) linkedin 3) watsapp

He estimate that he can get 100 students from facebook group,50 students from linkedin and 10 students from watsapp group.But he need to spend $20 per advertisement on facebook,$15 per advertisement on linkedin and $10 per advertisement on watsapp for his marketing agency whom he had hired for this work.There are few more restriction for him like by not allowing him to place more than 10 advertisement posts in facebook,5 advertisement posts in linkedin and another 5 posts in watsapp group in a month by his marketing agency.

In order to use balanced use of advertisement media,linkedin advertisement posts is again can not exceed 50% of the total advertisement posts that he is planning in any month.The total promotional budget he can spend in a month is maximum to the tune of $ 1000.With this constraints in mind,above Statistics Tutor can formulate above as linear programming problem with three decision variables x1,x2,x3 which denotes number of advertisement posts that he can place in each media ie facebook,linkedin and watsapp respectively in order to maximize his total students enrollment in any month. ie

Maximize 100x1+50x2+10x3 => This is known as Objective Function in Linear Programming

subject to 20x1+15x2+10x3 <=1000

x1 <=10

x2 <=5

x3 <=5 => These are known as constraints

x2 <= 0.5(x1+x2+x3)

and x1,x2 and x3 >=0

Such type of linear programming problems can be solved for optimal solution for x1,x2 and x3 using Excel Solver tool that come as built add-in that can installed with few clicks of button to find solution.

2)Sensitivity Analysis is important in linear programming modelling in order to find the changes in objective function by adding or modifying existing constraints  in order to find what-if type of scenario questions to find alternate solutions.For example, in the above problem,we may ask if budget is getting increased from $1000 per month to $2000 per month,what will be effect on number of advertisements posts for each media like facebook,linkedin and watsapp etc.Secondly,it also provide answers to resource constraint changes like for example in future,marketing agency is ready increase its posts in some of the advertisement media like facebook,in that case how many more students enrollments can get increased for statistics teacher in a month by getting answers from this sensitivity analysis.