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Chapter 15: Limiting factors and linear programming
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Total contribution = $11,000. (Calculated earlier, in the previous example)
Point D
At point D we have the equations:
(1) 4x + y
= 4,000
(2) y
= 0
Substitute (2) in equation (1) 4x
= 4,000
x
= 1,000
Total contribution = $5 × 1,000 = $5,000.
The total contribution at each point should be compared. This shows that total
contribution is maximised at Point C.
3.6 Linear programming: problems with more than two variables
A linear programming problem can have more than two variables. Problems with
more than two variables are formulated in exactly the same way as problems with
two variables. The only difference is that the objective function and the constraints
include more than two variables.
A linear programming problem with more than two variables cannot be solved by a
graphical method, however, and another solution method is used. A non-graphical
method of solving linear programming problems is the simplex method, but you do
not need to know this method for your examination.
Practice multiple choice questions
1 A company manufactures two products S and T using the same materials and
labour. It holds no inventories. Information about the variable costs and maximum
sales demand for each product are as follows:
Product S Product T
$/unit $/unit
Material ($5 per kg) 12 10
Labour ($20 per hour) 45 30
units units
Maximum sales per month 4,000 6,000
Each month a maximum of 21,500 kilograms of material and 18,200 hours of labour
are available.
Which one of the following statements is correct?
A Material is a limiting factor but labour is not a limiting factor
B Labour is a limiting factor but material is not a limiting factor
C Both material and labour are limiting factors
D Neither material nor labour is a limiting factor (2 marks)