myz-vgb.ru A Business Encyclopedia

Formulation of Linear Programming-Maximization Case

Definition: Linear programming refers to choosing the best alternative from the available alternatives, whose objective function and constraint function can be expressed as linear mathematical functions.

Maximization Case: Let’s understand the maximization case with the help of a problem. Suppose a firm produces two products A and B. For producing the each unit of product A, 4 Kg of Raw material and 6 labor hours are required. While, for the production of each unit of product B, 4 kg of raw material and 5 labor hours is required. The total availability of raw material and labor hours is 60 Kg and 90 Hours respectively (per week). The unit price of Product A is Rs 35 and of product, B is Rs 40.

This problem can be converted into linear programming problem to determine how many units of each product should be produced per week to have the maximum profit. Firstly, the objective function is to be formulated. Suppose x1 and x2 are units produced per week of product A and B respectively. The sale of product A and product B yields Rs 35 and Rs 40 respectively. The total profit will be equal to

Z = 35x1+ 40x2 (objective function)

Since the raw material and labor is in limited supply the mathematical relationship that explains this limitation is called inequality. Therefore, the inequality equations will be as follows:

Product A requires 4 kg of raw material and product B also requires 4 Kg of Raw material; thus, total consumption is 4x1+4x2, which cannot exceed the total availability of 60 kg. Thus, this constraint can be expressed as:

4x1 + 4x2 60

Similarly, the second constraint equation will be:

6x1 + 5x2 90

Where 6 hours and 5hours of labor is required for the production of each unit of product A and B respectively, but cannot exceed the total availability of 90 hours.

Thus, the linear programming problem will be:

Maximize Z = 35x1+ 40x2 (profit)

Subject to:

4x1 + 4x2 60 (raw material constraint)
6x1 + 5x2
90 (labor hours constraint)
x1, x2
0 (Non-negativity restriction)

Note: It is to be noted that “≤” (less than equal to) sign is used as the profit maximizing output may not fully utilize all the resources, and some may be left unused. And the non-negativity condition is used since the x1 and x2 are a number of units produced and cannot have negative values.

Leave a Reply

Your email address will not be published.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

Shares

Related pages


equity theory of motivation definitionpavlov classical conditioning theorydeterminants elasticity of demandpavlov's theory of classical conditioninglikert management systeminformal groups in organizationsdifferent types of segmentation in marketingexample of demand depositnarrow meaning in hindidefine regiodefine commercialseffective delegation of authoritydefinition stratifyrbi msfindifference analysis definitionsampling defdemand segmentation definitionadvantages of hrpdefine profit margin ratiotaylorism definitionasset utilisation ratio formuladeontological and teleological ethical theoryfayol's 14 principlesrevitalize meansdefinition classical conditioning7cs of business communicationjudgemental meansutil economicsstratification statistics definitionsystematic sampling in statisticsinformal and formal communicationfeatures of debenturesdiminishing utility definitioninvoluntary unemployment definitionstraddle meaning in urduexplain the difference between accounting profit and economic profitinformal communication meaningdelphi analysissubsitution methodnonbank financial companyportors five forcesinternal sources of secondary researchmotivation theory by herzberghezberg theoryvalence motivationmeaning of rbiwhat are the ethical theories in businessego states transactional analysisneed for business process reengineeringsnowballing definitiondefinition of host country nationalstux definitiondefinition of geocentricmonetarism theoryturnover ratio calculationsbu swhat is the definition of an oligopolywhat are the determinants of elasticityscalar chain principle of managementbarometric indicatorsregiocentric orientationwhats a moratoriumwhat is job enlargement with exampletypes of sbuinstrumental conditioning in marketingdescribe the difference between convenience sampling and quota samplinglpp modeldefine bookeddefine internationalizationtransportation problem linear programmingnet present value and profitability indexdifference between strata and stratumsaving certificatespayback methodlpc fiedlerformal groups and informal groups14 principal of henri fayolthe margin of safety percentage is computed asanti takeover strategiesbrand salience meaningtrainings meaningdef of delegate