Introduction Linear programming is a mathematical process of optimization by which one minimizes or maximizes a given function known as the objective function, subject to a finite number of linear constraints, which may be in the form of equations or inequalities (Karloff, 2008)…
The applications of linear programming span providing solutions to problems involving economics, computer science, and practically any other industry that requires a production schedule or an actual scheduling process. Moreover, the optimizing feature of linear programming makes it a necessity for people in the management circle to be familiar with. Simplex algorithm A linear programming model is typically solved using a simplex algorithm, or sometimes also referred to as the linear solver (Powell & Baker, 2010). The simplex algorithm involves a series of steps which employs the use of slack and basic variables to change the inequality constraints to equations so that the derived system of equations may be solved to find a feasible solution area. The extreme points of this feasible solution area are then tested by plugging them in to the objective function in order to find out which gives the optimal solution (Singiresu, 2009). Linear Programming Models There are a number of models that may be used to generate the solution to a linear programming model. ...
Such models are generally used in manufacturing companies or supply chain networks. Another kind of linear programming model involves the blending of a number of resources to produce desired results, hence the term blending model (Baker, 2011). A typical example of this model is the “diet problem” wherein one aims to find the optimum mix of food products that will produce the maximum nutritional value. The covering model of linear programming is quite different from the first two models in such that it aims to minimize the objective function and is presented with “greater than constraints” (Powell & Baker, 2010, p. 79). This model is commonly used when minimizing a cost function and requiring the contributions to be greater than a particular value. Finally, the network model is quite unique in nature as it “describes configurations of flow in a connected system” (Baker, 2011, p. 71). Typically, a network model would require the use of a diagram which aids in the finding of the optimal solution of a given problem. In all these types of linear programming models, spreadsheets may be used to provide assistance in finding the optimal solution. Excel has a built in Solver application which allows the user to simply input the coefficients of the objective function and constraints, and automatically generates values for the feasible region and the corresponding optimal solution. Sensitivity Analysis It should be noted that the task is not yet done when the optimal solution is found. It is also necessary to conduct a corresponding sensitivity analysis on the solution generated. Sensitivity analysis provides information on how instantaneous changes in the parameters of the problem would affect the optimal solution ...
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(Linear Programming Essay Example | Topics and Well Written Essays - 750 Words)
“Linear Programming Essay Example | Topics and Well Written Essays - 750 Words”, n.d. https://studentshare.net/logic-programming/48877-linear-programming.
Introduction Advertising and programming fall under commercial television. Advertising and programming does not only promote the advertisements or the programme that one is watching they also contribute widely in changing ones beliefs mood and attitude about a particular thing or a particular activity.
A typical LP problem would be to optimize which is subject to the following conditions: In these circumstances the variables x, y and z could represent material costs and labor costs respectively while z represents optimal cost. In order to set up a LP problem the inequalities are graphed and the corner points of the bound region are calculated.
In this situation, the independent variable is the early release of prison inmates. The early release of prison inmates qualifies to be the independent variable since the number of inmates released can be changed or manipulated in accordance with the relevant conditions.
For instance, when the number of hours worked increase so does the income. The correlation between the variables was moderate and positive, r = 0.3, If r is close to 0, it implies that there is less or no relationship between the variables (Bryman and Cramer, 1990).
Life is mixture of all types of function. Every thing we do is related to some other thing in our life in one or other way, linearly or nonlinearly. As an example duration for which our phone work is inversely proportional to the number of minutes you spend on the phone.
Symbols and numbers alone do not suffice; additionally, the logic of reasoning behind those numbers and symbols is also required. Scientific decisions arrived through the use of mathematical tools and statistical techniques should have an intuitive appeal and logical support, otherwise, the manager will be in trouble.
The model has been solved using a manual graphical approach to find the optimal values of quantities of two products and the maximum profit. A sensitivity analysis has been done to help Brass Ltd. take decision on increasing available capacity. Finally, a
Object programming on the other hand refers to a programming technique that is founded on the aspects of data structures which imbibe the data (Hughes, 2009). It is important to note and record that the data exist in