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Linear programming
2. A company workshop manufactures time. Each day there are 30 hours
tables and chairs. Each table of machine time and 60 hours of
requires 4 hours of labour from craftsman time. The profit on each
the construction department item type A chair is Tshs 2,330 and
and 2 hours of labour from the on each type B chair is Tshs 1,890.
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finishing department. Each chair Formulate a linear programming
requires 3 hours of labour from problem for maximizing the profit.
the construction department and 1 5. Mr Juma produces two packages
hour of labour from the finishing of fruits. Package A contains 20
department. A full working week peaches, 15 apples, and 10 pears.
has 140 hours of construction time Package B contains 10 peaches, 30
and 100 hours of finishing time. apples, and 12 pears. He has 40,000
Each table produced gives a profit peaches, 60,000 apples, and 27,000
of Tshs 3,250 and each chair gives a pears available for packaging. He
profit of Tshs 3,165. Formulate this earns a profit of Tshs 5,000 for
problem as a linear programming selling each item of package A and
problem for maximizing the profit. Tshs 7,000 for selling each item
3. A workshop prints two circuits of of package B. Formulate a profit
types C and C . Type C requires maximization linear programming
2
1
1
20 resistors, 10 transistors, and problem.
20 capacitors. Type C requires 6. A chef wishes to mix type I and
2
10 resistors, 10 transistors, and type II foods, in such a way that the
30 capacitors. The workshop mixture contains at least 10 units
has a stock of 200 resistors, 120 of vitamin A, 12 units of vitamin
transistors, and 150 capacitors.
B, and 8 units of vitamin C. The
Mathematics for Secondary Schools 4. A certain company manufactures of the two types of food is given
The profit on each item of type C
vitamin contents of one kilogram
1
circuit is Tshs 4,450 and Tshs 3,570
on each item of type C circuit.
in the following table.
2
Formulate the linear programming
Vitamin in kilograms
problem for maximizing the profit.
Food
A
B
C
Type I
3
2
1
two types of garden chairs. An
2
Type II
1
2
item of type A requires 2 hours
of machine time and 5 hours of
Tshs 2,500 and one kilogram of
craftsman time. An item of type If one kilogram of type I food costs
B requires 3 hours of machine type II food costs Tshs 2,850,
time and 5 hours of craftsman formulate a linear programming
problem to minimize the cost.
64 Student\s Book Form Three
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MATHEMATIC F3 SB.indd 64 18/09/2025 09:59:08
MATHEMATIC F3 SB.indd 64
