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Linear programming

Example 3.2

The labour charge for two professional tailors, A and B are Tshs 80,000 and Tshs
100,000 per day, respectively. Tailor A can make 6 shirts and 4 pairs of trousers
per day, while tailor B can make 10 shirts and 4 pairs of trousers per day. The
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tailors intend to produce at least 60 shirts and 32 pairs of trousers. Formulate a
linear programming problem which minimizes the labour cost involved.

Solution
The given information are summarized as shown in the following table.

Products Tailor A Tailor B Minimum requirements

Shirts 6 10 60
Pair of trousers 4 4 32
Labour cost per day (Tshs) 80,000 100,000

Let: x be the number of days professional tailor A works, and
y be the number of days professional tailor B works.

Thus, the objective function is given by;

Minimize f ( ,xy ) 80000x= + 100000y
The constraints are:

6x + 10y ≥ 60

4x + 0, y ≥ 4y ≥ 32
Mathematics for Secondary Schools Subjecto 6 t : x + 0, y ≥ 10y ≥ 0 60 ⇒ + 100000y 30
x ≥
0
Therefore, the linear programming problem is;
) 80000x=
( ,xy
Minimize f
5y ≥
3x +
y
8
2 3 ⇒+ ≥
x
4y ≥
4x +
x ≥
Example 3.3
Antonia wishes to blend two types of drinks, D and D in such a way that the
1
2
vitamin content of the mixture is at least 8 units of vitamin A and 11 units of
vitamin B. Type D costs Tshs 8,880 per litre and type D costs Tshs 11,840 per
1 2

62 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 62
MATHEMATIC F3 SB.indd 62 18/09/2025 09:59:07