A Business Encyclopedia

Formulation of Linear Programming-Minimization Case

Definition: Linear programming is a technique for selecting the best alternative from the set of available alternatives, in situations in which the objective function and constraint function can be expressed in quantitative terms.

Minimization Case: The minimization case can be well understood through a problem. Let’s say; the agricultural research institute recommended a farmer to spread out at least 5000 kg of phosphate fertilizer and not less than 7000 kg of nitrogen fertilizer to raise the productivity of his crops on the farm. There are two mixtures A and B, weighs 100 kg each, from which these fertilizers can be obtained.

The cost of each Mixture A and B is Rs 40 and 25 respectively. Mixture A contains 40 kg of phosphate and 60 kg of nitrogen while the Mixture B contains 60 kg of phosphate and 40 kg of nitrogen. This problem can be represented as a linear programming problem to find out how many bags of each type a farmer should buy to get the desired amount of fertilizers at the minimum cost.

Firstly, the objective function is to be formulated. Suppose, x1 and x2 are the number of bags of mixture A and mixture B. The cost of both the mixture is 40x1 + 25x2 and thus, the objective function will be:


Z = 40x1+25x2

In this problem, there are two constraints, minimum 5000 kg of phosphate and minimum 7000 kg of nitrogen is required. The Bag A contains 40 kg of phosphate while Bag B contains 60 kg of phosphate. Thus, the phosphate constraint can be expressed as:

40x1 + 60x2 5000

Similarly, the second constraint equation can be expressed as:

60x1 + 40x2 7000

Where, Bag A contains 60 kg of nitrogen and Bag B contains 40 kg of nitrogen, and the minimum requirement of nitrogen is 7000 kg.

Thus, the linear programming problem is:

Minimize Z = 40x1+25x2 (cost)

Subject to:

40x1 + 60x2 5000 (Phosphate Constraint)
60x1 + 40x2
7000 (Nitrogen Constraint)
x1, x2
0 (Non-negativity Restriction)

Note: It is to be noted that, “” (greater than equal to) sign shows the full utilization of resources at the minimum cost. The non-negativity condition is used, since x1 and x2 represent the number of bags of both the mixture and hence cannot have the negative values.

Leave a Reply

Your email address will not be published. Required fields are marked *


Related pages

how do you prepare a cash budgetjob enlargement definitionexamples of denotative wordstheory x and theory y by douglas mcgregormeaning of rationingneoclassic theoryboom and bust cycle definitionpavlovian learning definitionturnaround strategy definitioncrr in bankcobb douglas isoquantmargin lending definitionexplanation of 14 principles of management henri fayol with examplesforeign exchange speculationmarginal utility of xmanaging channel membersdefinition of investituredefinition stratified samplingbusiness jargons listwhat are virtues in ethicsabout henri fayolnnp gnpproduct mix pricing strategies with examplescheques definitioningredient branding definitioninstallment purchase definitionmarketing segmentation basesdefine retailstheory x and theory y in organizational behaviorwhat is meaning of spam in hindiquota samplesdefine captivesamuelson theorystock market speculator definitionspot currency transactiongdp nnpdefine a debentureexplanation of 14 principles of management henri fayol with examplesrecruitment process hrmapprenticeship training definitionaccelerator principlethe bottom up method for forecasting salesdivestiture defwhat is scatter diagramtridimensional theorydivestment meaning in hindiclassical conditioning meaningteleological theories of ethicsmeaning of lafcorporate vertical marketing system definitionclassical scientific management theorydivestiture company exampleswhat is an autocratic leadershipsituational contingencyblack scholes d1 d2correlation karl pearson methodcontractual marketing systemspeculation definition economicscarrot incentiverevitalized meaningdefine cultural ethnocentrismsfa automationindifference curve convexindifference curves economicswhat is judgement samplingoutflank definitionmeaning of pure competitiondavid mcclelland theory of needswhat is the meaning of neftrepo and reverse repo meaningwhat is cash reserve ratiowhistle blowing conceptboom and bust cycle definitionlikert management styles