Linier Programming. By Agustina Shinta. What is it?. LP is essentially a mathematical technique for solving a problem that has certain characteristics.
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LP is essentially a mathematical technique for solving a problem that has certain characteristics.
There is a function or objective to be maximized or minimized, there are limited resources to be used in the satisfaction of this objective, and numerous means of using the resources are available
Farmers may have : land, machinery and equipments and labor resources that they can use to produce corn, soybeans, wheat, hay, oats and other crops, and they would like to combine these resources in such a fashion as to maximize net income.
Although most farm management applications of LP involve short run planning where resource supplies are fixed, long run planning where additional resources can be acquired over time can be done with LP
LP can be used industrial sector such as transportation, petroleum, and meatpacking industries and other sectors involving production, transportation and distribution of goods and services.
The technique is also being used extensively in the planning of individual farm business through the use of prerestructured LP packages that are available through many extension services.
LP have been well tested and proven applicable to a wide variety of problems in the farm and business management area
LP is a set of mathematical rules for solving specific problems. Standard computer programs are available to accomplish these tasks.
The reasons for studying LP are numerous
First, the procedure is applicable to almost any resource allocation problem faced by the farm manager.
This ability to handle different issues with one analysis procedure means that time allocated to understanding the procedure can be “spread over many potential uses”
Second, the procedure can handle more complex problems than budgeting or marginal analysis. We can specify more complex, realistic problems without concern for the cost or feasibility of obtaining an answer
Third, LP provide not only information on the best or optimal way of allocating resources and the best production marketing financial plan, but also additional information concerning the value of various resources used in that plan.
Ex : budgeting or marginal analysis. We can specify more complex, realistic problems without concern for the cost or feasibility of obtaining an answer
LP would indicate :
Fourth, It can easily be used to evaluate how the results would change it changes occurred in product prices or technical efficiency- the sensitivity or stability of the farm plan.
Fifth, it handles the issues of “opportunity cost”. It can reflect income forgone in using a resource in an alternative enterprise
In sum up, LP is one of the few techniques available that can solve a realistically defined farm management problem using mathematical procedures consistent with the economic concept of marginal analysis.
A process is a method of transforming resources or inputs into a specific output.
Although this definition sound quite similar to that of a production function, a process is much more restrictive in that the relative proportion of all inputs and outputs is fixed in a process.
It implies that there are many alternative ways to produce a single product in a LP model.
In addition to determining the optimal combination of products or enterprises to include and the allocation of scarce resources to those enterprises, the LP procedure can also indicate the optimal technology or method of production that should be used.
4 basic assumptions are
The assumption specifies a limit to the number of alternative processes and resource restrictions that can be included in the analyisis.
Farm managers can only allocate so much time to the evaluation of alternatives and must restrict their analysis to a subset of the possible production and marketing alternatives available of them.
This assumption specifies that resource supplies, input output coefficients, and commodity and input prices must be known with certainty
Linearity of production relationships
Completely divisible outputs and inputs
A finite set of production alternative
Single valued expectations of prices and production efficiencies