Linear Programming
TOPIC – LINEAR PROGRAMMING
Linear Programming is a mathematical procedure for determining optimal allocation of scarce resources. Requirements of Linear Programming
• all problems seek to maximize or minimize some quantity
• The presence of restrictions or constraints
• There must be alternative courses of action
• The objective and constraints in linear programming must be expressed in terms of linear equations or inequalities Objective Function it maps and translates the input domain (the feasible region) into output range, with the two-end values called the maximum and minimum values Restriction Constraints it limits the degree to which we can pursue our objective Decision Variables represents choices available to the decision maker in terms of amount of either inputs or outputs Parameters these are the fixed values in which the model is solved Basic Assumption of Linear Programming 1. Certainty- figures or number in the objective and constraints are known with certainty and do not vary 1. Proportionality - for example 1:2 is equivalent to 5:10 1. Additivity - the total of all the activities equals the sum of the individual activities. 1. Divisibility - solutions to the LP problems may not be necessary in whole (integers) numbers, hence, divisible and can assume any fractional value 1. Non-negativity - cannot use or produce negative physical quantities. Procedures in Graphical Solution 1. Set up the objective function and constraints in mathematical format. 1. Plot the constraints 1. Identify the feasible solution space 1. Plot the objective function 1. Determine the optimum solution Sample Problem Set Department Tables ( T ) Chairs (
Linear Programming is a mathematical procedure for determining optimal allocation of scarce resources. Requirements of Linear Programming
• all problems seek to maximize or minimize some quantity
• The presence of restrictions or constraints
• There must be alternative courses of action
• The objective and constraints in linear programming must be expressed in terms of linear equations or inequalities Objective Function it maps and translates the input domain (the feasible region) into output range, with the two-end values called the maximum and minimum values Restriction Constraints it limits the degree to which we can pursue our objective Decision Variables represents choices available to the decision maker in terms of amount of either inputs or outputs Parameters these are the fixed values in which the model is solved Basic Assumption of Linear Programming 1. Certainty- figures or number in the objective and constraints are known with certainty and do not vary 1. Proportionality - for example 1:2 is equivalent to 5:10 1. Additivity - the total of all the activities equals the sum of the individual activities. 1. Divisibility - solutions to the LP problems may not be necessary in whole (integers) numbers, hence, divisible and can assume any fractional value 1. Non-negativity - cannot use or produce negative physical quantities. Procedures in Graphical Solution 1. Set up the objective function and constraints in mathematical format. 1. Plot the constraints 1. Identify the feasible solution space 1. Plot the objective function 1. Determine the optimum solution Sample Problem Set Department Tables ( T ) Chairs (