Page 70 - Mathematics_Form_3

Linear programming

litre. Type D contains 3 units of vitamin A per litre and 5 units of vitamin B
1
per litre, while type D contains 4 units of vitamin A per litre and 2 units of
2
vitamin B per litre. Formulate a linear programming problem to minimize the
cost of the mixture.
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Solution
The given information is summarized as shown in the following table.
Minimum
Drinks
Vitamin requirements (Units)
D D
1 2
A 3 4 8
B 5 2 11

Cost (Tshs) per litre 8,880 11,840
Let: x be the number of litres of drink type D , and
1
y be the number of litres of drink type D .
2
Thus, the objective function is given by;

Minimize f ( ,xy ) 8880x= + 11840y
The constraints are:
3x + 4y ≥ 8
5x + 2y ≥ 11
x ≥ 0, y ≥ 0

Therefore, the linear programming problem is;
Minimize f ( ,xy ) 8880x= + 11840y
Subject to: 3x + 4y ≥ 8
5x + 2y ≥ 11

x ≥ 0, y ≥ 0

Exercise 3.1 Mathematics for Secondary Schools

1. A paint factory makes two types of paint, standard quality P and high
1
quality P . In order to manufacture these paints, two ingredients, dye and
2
pitch are needed. P requires 2 units of dye and 3 units of pitch for each unit
1
made, and it is sold at a profit of Tshs 2,000. P requires 4 units of dye and
2
2 units of pitch for each unit made, and it is sold at a profit of Tshs 2,500.
The factory has stocks of 12 units of dye and 10 units of pitch. Formulate a
linear programming problem to maximize the profit.

Student\s Book Form Three 63

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MATHEMATIC F3 SB.indd 63 18/09/2025 09:59:08
MATHEMATIC F3 SB.indd 63