QUANTITATIVE METHODS FOR BUSINESS

Quantitative Methods for Business

Quantitative Methods for Business

Answer No. 1

In order to find the optimal solution, it is important to evaluate the objective function for the feasible solution, which is presented below:

Feasible Region

Profit Line

The objective is to find the feasible solution with the maximum contribution to the profit, for that reason, it is important and necessary to select maximum profit contribution, which is shown as the feasible region.

Answer No. 2

Linear Programming

Modern society, especially the economy is faced daily with a variety of complex tasks, which can have multiple solutions. The logical question that arises is how to get the best is the optimal solution. In addressing these tasks has been applied above a minimum or maximum, which means maximizing profit with minimal investment (Al-Shammari & Dawood, 1997). The first step in solving a problem is the establishment of a mathematical model. It comprises the objective function and constraints. Therefore, the task is to determine the maximum or minimum of the objective function to specify a set of constraints (Earnshaw, Hicks, Richter & Honeycutt, 2007). Depending on the type of functions are described, problems can be linear or nonlinear. The linear problem is a problem in which the objective function and linear constraints which are all represented by linear functions. Linear problem is a special case of nonlinear problems. If the objective function is non-linear, or if at least one of the constraints in a nonlinear function, it is a nonlinear problem. In addition to this, the optimization problem of linear programming consists of the following:

One or more x-variables (decision variables to control over);

Normally, a number of constraints that must be met (similarities and / or differences). That is, constraints or relation between the x variables;

An objective function, f (x), whose maximum or minimum is sought.

Furthermore, the problem of linear programming is an optimization problem, where the objective function is linear. In relation to this, constraints must be linear differences or similarities). Usually, we have constraints on the decision variables must be non-negative. If we assume that the constraints limiting the size of all the decision variables in a linear programming problems, there are maximum and minimum of one or sometimes any of the corners of the allowed range. In addition to this, for easy access and visual inspection of any general properties of linear programming problems will first be presented to the graphical method for solving linear programming problems in two-dimensional cases that are feasible region and profit line (Mathieu, 2006). Moreover, a linear programming problem (LP) may have a unique solution that is optimum in a corner, many solutions which reflects optimum at a boundary, that are several corners are as good, no solution which shows constraints allow nothing, that is unreasonable or incorrect requirements and an unlimited solution which shows constraints do not limit the solution, probably we have missed any limitation or waiting any difference wrong way (Zlobec, 2001).

Answer No. 3

Foster should produce and ship from each plant to each distribution center, in accordance with the ...