CHAPTER 7: DEVELOPING THE LINEAR PROGRAMME AND SOLVING GRAPHICALLY
CHAPTER 7: DEVELOPING THE LINEAR PROGRAMME AND SOLVING GRAPHICALLY
TOOLS REQUIRED TO SOLVEA LINEAR PROGRAMMING ◆ linear functions o graphs and co-ordinate systems representing linear functions graphical o solving simultaneous linear equations o Software package-MS-Excel Solver
TOOLS REQUIRED TO SOLVE A LINEAR PROGRAMMING linear functions graphs and co-ordinate systems representing linear functions graphically solving simultaneous linear equations Software package—MS-Excel Solver
FORMULATING THE LINEAR PROGRAMMING t The definition of the decision variables Let x= the number of fables manufactured per week Let y= the number of chairs manufactured per week The objective function Maximise profit =4X+3Y
FORMULATING THE LINEAR PROGRAMMING The definition of the decision variables – Let X = the number of Tables manufactured per week – Let Y = the number of Chairs manufactured per week The objective function – Maximise Profit = 4X + 3Y
The set of constraints 4X+lY<90 Constraint due to Wood 2X+lY<50 Constraint due to Machine-Time] 1X+ lY<40 [Constraint due to Polishing-Timel X20, Y20 [non-negative constraint
The set of constraints – 4X + 1Y 90 [Constraint due to Wood] – 2X + 1Y 50 [Constraint due to Machine-Time] – 1X + 1Y 40 [Constraint due to Polishing-Time] – X0, Y 0 [non-negative constraint]
◆ SUMMARY Let X=the number of Tables made per week Let y= the number of Chairs made per week Maximise Profit =4X+3Y Objective Function Subject to 4X+1Y≤90 Wood 2X+1Y≤50 Machine-Time X+1Y≤40 Polishing-Time X,Y≥0
SUMMARY – Let X = the number of Tables made per week, Let Y = the number of Chairs made per week, – Maximise Profit = 4X + 3Y Objective Function Subject to 4X+1Y 90 Wood 2X+1Y 50 Machine-Time 1X +1Y 40 Polishing-Time X, Y 0