Please answer the following questions in detail and substantive paragraphs: 1. I
ID: 456038 • Letter: P
Question
Please answer the following questions in detail and substantive paragraphs:
1. It is important to understand the assumptions underlying the use of any quantitative analysis model. What are the assumptions and requirements for an Linear Programming model to be formulated and used?
2. Under what conditions is it possible for an Linear Programming model to have more than one optimal solution?
3. Discuss what was learned from the You Tube video: https://www.youtube.com/watch?v=RicajFzoenk&feature=youtu.be
Explanation / Answer
1. Linear programming deals with the optimization (maximization and minimization) of a linear function of a number of variables subject to a number of conditions on the variables, in the form of linear inequations or equations in variables involved. The inequalities or equalities are called the constraints and the function to be maximized or minimized is called objective function.
LInear programming is used to represent a firm's decisions, given business objectives and resource constraints. Following are the assumptions given:
a) The objective function and the constraints are linear.
b) Values of decision variables can be fractions or non-integer. Moreover, there is no interaction between decision variables.
c) Responses to the values of variables are equivalent to the responses to the coefficient.
d) Data is always available to specify the problem.
e) There will be proportional change in the value of objective function in case there is change in the constraint inequilities.
f) Decision variables are in continuity.
g) Information given in a linear programming model is certain.
Linear programming problem formulation:
A. First, we identify the objective of the problem.
B. Then, decision variables and constraints are identified and written.
C. Add non-negative restrictions if any.
D. All the equations are arranged in a consistent form.
E. Mathematical model is formulated and solved.
Linear programming model is used to solve numerous problems in the field of business operations and administration. Following are the areas where linear programming model is used:
1. Product mix planning
2. Distribution networks
3. Staff or labor scheduling
4. Transportation Routing
5. Optimal product line
6. Diet problems
7. Financial portfolios
8. Corporate restructuring
9. Highlights bottlenecks, if occured
Linear programming model is required to solve maximization or minization of the quantity, generally profit or cost.
2. A solution of a linear programming problem (LPP) which satisfies the non-negativity restrictions of the problem is called its feasible solution. A feasible solution which optimizes the objective function of a LPP is called an optimal solution of the LPP. A LPP may have many optimal solutions. If a LPP has two optimal solution, then there are an infinite number of optimal solutions. This situation occurs when the objective function has same slope.