Everything Maths Grade 11

15.5 CHAPTER 15. LINEARPROGRAMMING

Example 2: Writing the objective function

QUESTION

The cost of hiring a small trailer is R 500 per day and the cost ofhiring a big trailer is R 800 per
day. Write down the objective function that canbe used to find the cheapest cost for hiring
trailers for one day.

SOLUTION

Step 1 : Identify the decision variables

There are two decision variables:the number of small trailers (m) and the number

of big trailers (n).

Step 2 : Write the purpose of the objective function

The purpose of the objective function is to minimise cost.

Step 3 : Write the objective function

The cost of hiring m small trailers for one day is:

500 × m

The cost of hiring n big trailers for one dayis:

800 × n

Therefore the objectivefunction, which is the total cost of hiring m small trailers

and n big trailers for one dayis:

(500× m) + (800× n)

Example 3: Writing the objective function

QUESTION

Mrs Nkosi expects to make a profit of R 650 per m^2 for her mielies and R1 500 per m^2 on her
potatoes. How should she divide her land so that she can earn the most profit?