CHAPTER 6: LINEAR PROGRAMMING NTRODUCTION INPUTS OUTPUTS FACTORY BUSNESS OBJECTTES Figure I
CHAPTER 6:LINEAR PROGRAMMING INTRODUCTION
5+ INPUTS: Resource: Raw material Labour. and how much of each resource FACTORY: Production process: how much of each of the inputs per unit output OUTPUTS: What products to manufacture THE BUSINESS OBJECTIVE: To maximise profit, to minimise costs
INPUTS: Resource: Raw material, Labour…and how much of each resource FACTORY: Production process: how much of each of the inputs per unit output. OUTPUTS: What products to manufacture. THE BUSINESS OBJECTIVE: To maximise profit, to minimise costs
W Example Product Wood Machine- Polishing Unit Time Time Pr Table 4 Kilos 2 Hours nour Chair I Kilo Resource 50 40 What production policy should the company adopt to make the maximum profit?
Example What production policy should the company adopt to make the maximum profit? Product Wood MachineTime PolishingTime Unit Profit Table 4 Kilos 2 Hours 1 hour £4 Chair 1 Kilo lHour lHour £3 Resource 90 50 40
OUTPUTS: Tables and Chairs INPUTS: The following resources with the availability as given WOOD: 90 Kilograms available per week MACHINE-TIME: 50 hours available per week POLISHING-TIME: 40 hours available per week l FACTORY One Table requires 4 Kilograms of Wood, 2 hours of Machine-Time and I hour of Polishing-Time One Chair requires 1 Kilograms of Wood, I hour of Machine-Time and I hour of polishing-Time A BUSINESS OBJECTIVE: How much is Tables and Chairs to be manufactured that leads to maximum profits
OUTPUTS: Tables and Chairs INPUTS: The following resources with the availability as given: – WOOD: 90 Kilograms available per week. – MACHINE-TIME: 50 hours available per week. – POLISHING-TIME: 40 hours available per week. FACTORY: – One Table requires 4 Kilograms of Wood, 2 hours of Machine-Time and 1 hour of Polishing-Time. – One Chair requires 1 Kilograms of Wood, 1 hour of Machine-Time and 1 hour of Polishing-Time. BUSINESS OBJECTIVE: How much is Tables and Chairs to be manufactured that leads to maximum profits
SOLVING THIS PROBLEM Graphical Solution an Intuitive Approach Stage 1: The set of all possible production plans that meet all the factory input constraints are evaluated Stage 2: From the set of all possible production plans the particular production plan that meets the business objective is found
SOLVING THIS PROBLEM – Graphical Solution an Intuitive Approach • Stage 1: The set of all possible production plans that meet all the factory input constraints are evaluated. • Stage 2: From the set of all possible production plans the particular production plan that meets the business objective is found