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WEEK-2 LINEAR PROGRAMMING Waheed Ullah PhD Scholar INU

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PRESENTATION OUTCOMES; WHAT IS LINEAR PROGRAM? OBJECTIVE/ PURPOSE OF LP CHARACTERISTICS/ WHERE TO USE? EXAMPLE

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What is LP? It is a Mathematical programming which is used to find the best or optimal solution to a problem that requires a decision or set of decisions about how best to use a set of limited resources to achieve a state goal of objectives.

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PURPOSE & OBJECTIVE SCARCE RESOURCES LP IS A METHOD OF ALLOCATING RESOURCES IN A OPTIMAL WAY LP IS A DECISION AIDING TOOL WIDELY USED IN INDUSTRY FOR DRAWING INFERENCE

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OBJECTIVE FUNCTION COSTS CAN BE MINIMIZED PROFITS CAN BE MAXIMIZED

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CHARACTERISTIC AND USAGE (Production Management) PRODUCT MIX TO DETERMINE THE QUANTITY OF EACH PRODUCT PRODUCTION PLANNING TO DETERMINE THE MINIMUM COST PRODUCTION PLAN WITH AN ITEM FLUCTUATIN DEMAND ASSEMBLY LINE BALANCING TO MINIMIZE THE TOTAL ELAPSE TIME

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PORTFOLIO SELECTION TO FIND THE ALLOCATION OF WHICH MAXIMIZES THE TOTAL EXPECETED RETURN OR MINIMIZE THE RISK UNDER CERTAIN LIMITATIONS PROFIT PLANNING MAXIMIZATION OF THR PROFIT MARGING FROM INVESTMENT IN PLANT FACILITIES AND EQUIPMENTS, CASH IN HAND, & INVENTORY (FINANCIAL MANAGEMENT)

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MEDIA SELECTION TO DETERMINE THE ADVERTISING MEDIA MIX SO AS TO MAXIMIZE THE EFFECTIVE EXPOSURE, SUBJECT TO LIMIT OF BUDGET, SPECIFIED EXPOSURE RATES TO DIFFERENT MARKET SEGMENT TRAVELLING SALESMAN PROBLEM TO FIND THE SHOR5TEST ROUTE FROM A GIVEN CITY TO EACH OF THE SPECIFIED CITIES & THEN RETURNING TO THE ORIGINAL POINT OF DEPARTURE, PROVIDED NO CITY WOULD BE VISITED TWICE (MARKETING MANAGEMENT)

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PHYSICAL DISTRIBUTION TO DETERMINE THE MOST ECONOMIC AND EFFICIENT MANNER OF LOCATING MANUFACTURING PLANT & DISTRIBUTION CENTRE FOR PHYSICAL DISTRIBUTION PROBLEMS (MARKETING MANAGEMENT)

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STAFFING PROBLEM TO ALLOCATE OPTIMUM MANPOWER TO A PARTICULAR JOB SO AS TO MINIMIZE THE TOTAL OVERTIME COST OR MANPOWER EQUITABLE SALARIES TO DETERMINE EQUITABLE SALARIES & SALES INCENTIVES JOB EVALUATION & SELECTION SELECTION OF SUITABLE PERSON FOR A SPECIFIED JOB (PERSONNEL MANAGEMENT)

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EXAMPLE A FURNITURE MANUFACTURES PRODUCES WOODEN TABLE & CHAIRS. UNIT PROFIT FOR TABLE – 6Rs/- UNIT PROFIT FOR CHAIR – 8Rs/- LETS ASSUME THERE ARE ONLY TWO RESOURCES COMPANY USES TO PRODUCE TABLE & CHAIR WOOD (BOARD FEET) LABOUR (HOUR)

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IT TAKES 30 WOOD & 5 HOURS TO MAKE A TABLE & 20 WOOD (BF) & 10 HOURS TO MAKE A CHAIR THERE ARE 300 BOARDFEET OF WOOD AVAILABLE & 110 HOURS OF LABOUR AVAILABLE THE COMPANY WISHES TO MAXIMIZE THE PROFIT (OBJECTIVE VARIABLE) RESOURCES (WOOD & LABOUR) ARE DECISION VARIABLES THE LIMITATION ON RESOURCES AVAILABILITY FORM THE CONSTRAINT

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SIMPLEX METHOD MOST COMMON WAY TO SOLVE THE LARGE LP PROBLEMS MATHEMATICAL TERM SIMPLEX IS A LINE SEGMENT CONNECTING TWO POINTS TWO DIMENSIONAL THREE DIMENSIONAL

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EXAMPLE LP FORMULATION RESOURCESTABLE (x1)CHAIR (x2)AVAILABLE WOOD3020300 LABOUR510110 UNIT PROFIT68-

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TO SIMULTENIOUSLY SOLVE THE TWO CONSTRAINT EQUATION, FIRST MULTIPLY THE LABOUR EQUATION BY -2, & ADD IT TO THE WOOD EQUATION 30x1 + 20x2 = 300 (WOOD) -2(5x1 + 10x2 = 110) (LABOUR) 20x1 + 0= 80 x1= 4 TABLES

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WOOD CONSTRAINT

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LABOR CONSTRAINT

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THANK YOU QUESTIONS ? IF ANY ?

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