Question

What is Linear Programming? Give an example of an application of Linear

Answer 1

DEFINITION:

Linear Programming (LP) is a method to achieve the best outcome, such as maximum profit or lowest cost in a Mathematical Model whose requirements are represented by linear relationships.

EXAMPLE OF APPLICATION:

Consider a farmer with:

a piece of farm land = L km²

to be planted with

(i) Wheat or

(ii) Barley.

A limited amount of fertilizer =F kilograms

A limited amount of pesticides = P kilograms

Every square kilometer of Wheat requires: F1 kilograms of Fertilizer and P1 kilogram of pesticides.

Every square kilometer of Barley requires: F2 kilograms of Fertilizers and P2 kilograms ofpesticides.

Let

S1 = Selling price of Wheat per square kilomter

S2 = Selling price ofBarley per square kilometer.

Let

x1 = area of land planted by Wheat

x2 = area of land planted by Barley

Then, Profit is maximized by choosing optimal values of x1 and x2.

This is written as a Linear Programming as follows:

Maximize:
R = S1 x1 + S2 x2 (MaximizeObjective Function: Revenue)

Subject to Linear Constraints:

x1+x2 L (Limit on Total Area)

F1 x1 + F2 x2 F (Limit on Fertilizer)

P1 x1 + P2 x2 P (Limit on Pesticide)

x1 0,   x2 0 (Non - negativity contraints)