Everything Maths Grade 11

15.5 CHAPTER 15. LINEARPROGRAMMING

15.5 Skills You Will Need

EMBCB

Writing Constraint Equations EMBCC

You will need to be comfortable with convertinga word description to amathematical description for

linear programming. Some of the words that areused is summarised in Table 15.1.

Table 15.1: Phrases andmathematical equivalents.

Words Mathematical description

x equals a x = a

x is greater than a x > a

x is greater than or equalto a x≥ a

x is less than a x < a

x is less than or equal to a x≤ a

x must be at least a x≥ a

x must be at most a x≤ a

Example 1: Writing constraints asequations

QUESTION

Mrs Nkosi grows mieliesand potatoes on a farmof 100 m^2. She has accepted orders that will

need her to grow at least 40 m^2 of mielies and at least 30 m^2 of potatoes. Market research

shows that the demandthis year will be at leasttwice as much for mielies as for potatoes and

so she wants to use at least twice as much area for mielies as for potatoes.

SOLUTION

Step 1 : Identify the decision variables

There are two decisionvariables: the area usedto plant mielies (q) and the area

used to plant potatoes (p).

Step 2 : Identify the phrases that constrain the decision variables

• grow at least 40 m^2 of mielies


• grow at least 30 m^2 of potatoes


• area of farm is 100 m^2


• demand is at least twice as much for mielies asfor potatoes

Step 3 : For each phrase, writea constraint