# Linear programming Report Harvard Case Solution & Analysis

Introduction
The linear programming refers to the maximization or minimization of the several variables such as the cost of manufacturing of a particular product, or the input costs or the output from the different machines having different constraints. It is a model that helps to understand different variables in different ways with some being independent and depended on one each other. In simpler definition, the linear programming is achieving the best outcome from the available variables and constraints, like maximizing the profit or the reducing cost.
Furthermore, the linear programming can be used in any field, when there are many variables depending on the input, and the best way is through using linear programing to get best outcome. Therefore, it is can also be used in constructing the data model representing the set of population from different category of population. Such as population from COPD having high risk of being exposed to disease and second is COPD patients. Meanwhile, this population is divided into three different age groups 25-44, 45-64, and 65+.
On the other hand, it can be determined that there are six programs also called as the intervention to provide counselling regarding the disease. Indeed, each program has different cost per person, and it is also important to know that each program provides QALY . Meanwhile, young age group has more benefit than any other group in the category. Similarly, each group member can also have membership in another group. Whereas, some groups have eligibility criteria regarding the age, or the type of person whether he has a disease, or he has higher risk.
Furthermore, there is demand and supply constraints in the case. However, the focus of the model is to understand the different models of the linear programs and understand the inputs in the caseand to develop a model that could lead to best available option to be utilized. Meanwhile, it is also objective to understand practically what and how budget have impacted on the intervention, and on the benefit of the intervention, and in which intervention the budget should be increased rather than other intervention having less benefit.
Problem statement
What is sufficient budget in given constraints and demand scenario since the quality adjusted life year is purpose of the case to maximize it and at what minimum budget would state be able to offer interventions to which group completely or partially?
Methods
The Excel solver is used to carry out the linear programming. However, the sum product formula has also been used in the methods while modeling. Furthermore, it can be determined that the excel solver is excel add-in that calculates the output based on the given scenario such as the demand and capacity constraints, and other variable inputs in the model. Furthermore, if we describe the model then the model consist of intervention, age group, population, and the budget.
On the other hand, the demand and constraints are constant throughout the modeling expected in some scenario. Indeed, the major independent variable is the budget of the intervention that is very important and is the focus of the program. Because, it effects the overall interventions in the model. Furthermore, the excel solver provides best outcome based on the given inputs, variables, and other constraints as well............

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