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Linear programming
and P requires 60 hours of machine hours on machine B. A table requires
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work. The maximum hours available 4 hours on machine A and 4 hours on
are 720. If the profit per tonne of machine B. There are 16 hours per
P is Tshs 14,670 and of P is Tshs day available on machine A and 20
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13,280, find the optimal solution by hours per day on machine B. Profits
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the graphical method. made by the carpenter for a chair
4. A farmer can buy two types of plant and a table are Tshs 4,000 and Tshs
food, F and F . Each cubic metre 3,000, respectively. What should be
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2
of F contains 30 kg of phosphoric the daily production of each of the
1
acid, 20 kg of nitrogen, and 20 kg two items in order to maximize the
of potash. Each cubic metre of F profit?
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contains 6 kg of phosphoric acid, 20 7. An agricultural company has 180
kg of nitrogen, and 8 kg of potash. tonnes of nitrogen fertilizers, 160
The minimum monthly requirements tonnes of phosphate, and 220 tonnes
are 120 kg of phosphoric acid, 200 of potash. The company will be able to
kg of nitrogen, and 120 kg of potash. sell 3:2:4 mixtures of these substances
If food F costs Tshs 55,000 per at a profit of Tshs 28,000 per tonne
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cubic metre and food F costs Tshs and 2:2:2 mixtures at a profit of Tshs
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70,000 per cubic metre, use the 30,000 per tonne, respectively. Use
graphical method to solve the linear the graphical method to determine
programming problem of minimizing the number of units of these two
the cost. mixtures that should be prepared so
5. A firm produces two products, P and as to maximize profit.
Q. The daily total production limit 8. A company manufactures two
is 600 units. The firm requires to products, X and Y. Each product has
Mathematics for Secondary Schools unit is 6 for P and 2 for Q. At least departments. Each unit of X takes
produce at least 300 units everyday.
to be processed in three departments:
Machine hours consumption per
Welding, assembling, and painting
1,200 machine hours must be used
2 hours in the welding department,
daily. Manufacturing costs per unit
3 hours in assembling, and 1 hour
are Tshs 1,500 for P and Tshs 850
in painting. The corresponding
for Q. Use the graphical method to
processing hours for a unit of Y
find an optimal solution of the linear
are 3, 2, and 1 hours, respectively.
programming problem.
month are 1,500 in welding, 1,500
6. A carpenter makes chairs and tables.
Production of these items is done The labour hours available in a
in assembling, and 550 in painting.
using machines A and B. A chair The contribution to profit and fixed
requires 2 hours on machine A and 4 overheads are Tshs 19,660 for product
74 Student\s Book Form Three
18/09/2025 09:59:13
MATHEMATIC F3 SB.indd 74
MATHEMATIC F3 SB.indd 74 18/09/2025 09:59:13
