Linear Programming — Part 1: Formulation and feasible regions: visual lesson, CBSE Class 12 Mathematics

Lesson

Linear Programming, Part 1: Setting up the problem

Limited flour, limited oven time — how many of each cake earns the most?

In this lesson you will

Use the terms decision variable, objective function, constraint and non-negativity
Formulate a linear programming problem from a short situation
Draw the half-plane of a linear inequality using a test point
Identify bounded, unbounded and empty feasible regions and list their corner points

$2x + y = 40$
$2x + 3y = 72$

The bakery's feasible region: a quadrilateral with four corners.

Concept

What you will be able to do

Name the parts of a linear programming problem (LPP)
Formulate an LPP from a short situation
Draw the region of a linear inequality with a test point
Find the feasible region and its corner points
Recognise bounded, unbounded and empty regions

Concept

Optimising under limits

We want the largest profit or the smallest cost, but every plan must respect limits on resources. When the goal and all the limits are linear, the problem is a linear programming problem.

Turn each row of the table into one line of the problem.
Resource	Sponge cake	Fruit cake	Available
Flour (g)	$300$	$150$	$6000$
Oven time (min)	$20$	$30$	$720$
Profit (₹)	$60$	$80$	—

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