Short slides on Basic s linear programming problem

1. Linear programming

2. Introduction of Linear Programming
● It is a mathematical programming technique to optimize
performance.
● (Eg. Maximization of profits or minimisation of costs , etc.)
● Under a set of resource, constraints (eg. Machine-hours, man-
hours,money , materials,etc ) as specified by an org.

3. Concept of Linear Programming
● An Objective function
● Set of constraints
● Non-negativity restrictions
● Decision Variables
● Technological coefficients
● Availability of resources

4. Q.1) A company manufactures 2 types of products P1 & P2. Each product uses lathe and
milling machine. The processing time per unit of P1 on the lathe is 5 hours and on the
milling machine, it is 4 hours. The processing time per unit of P2 on the lathe is 10 hours
and on the milling machine, it is 4 hours. The maximum number of hours available per
week on the lathe and the milling machine are 60 hours and 40 hours, respectively. The
profit per unit that the company can get on selling P1 & P2 are Rs.6 & Rs.8 per unit,
respectively. Considering the production volumes of the products P1 & P2 as x & y,
formulate this as a linear programming problem.