Page 85 - Mathematics_Form_3
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Linear programming
respectively to be painted. The examinations. If the student drinks
painting department is restricted more than 300 grams of caffeine,
not to use more than 240 minutes he will suffer heart palpitation and
a day. The company earns a profit fail his examinations. How many
of Tshs 10,000 and Tshs 20,000 cups of tea and coffee should the
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for types A and B machines, student drink to maximize his
respectively. correct answers?
(a) How many of each machine 7. Mr. Makungu plans to sow maize
should be produced for and beans in his farm. He estimates
maximum profit? to use 4 and 6 persons per hectare
(b) Find the maximum profit. of maize and beans, respectively
from 26 workers available. Sowing
5. A manufacturer has 24, 37, and maize and beans costs Tshs 12,000
18 tonnes of wood, plastics, and and Tshs 8,000 per hectare,
steel, respectively, for making respectively. If he is prepared to
two products, A and B. Product A spend up to Tshs 48,000, find the
requires 1, 3, and 2 tonnes of wood, largest possible area he can sow.
plastic, and steel, respectively.
Product B requires 3, 4, and 1 8. A carpenter's workshop in a certain
tonnes of wood, plastic and steel, college makes tables and chairs
respectively. If product A is sold which are processed through
at Tshs 400,000 and product B is assembling and finishing sections.
sold at Tshs 600,000, how many The college uses 48 hours in the
products of each type should the assembling section and 36 hours
manufacturer make to obtain the in the finishing section. A table
maximum gross income? requires 3 hours in the assembling
Mathematics for Secondary Schools will answer two extra questions in the finishing sections. If a chair
and 3 hours in the finishing
6. For each cup of coffee a student
sections, while a chair requires 4
drinks before examination, he
hours in the assembling and 2 hours
correctly. For each cup of tea he
makes a profit of Tshs 4,000 and
drinks, he will answer one extra
Tshs 5,000 for a table, how many
question correctly. A cup of coffee
chairs and tables should be made
has 10 grams of sugar and 100
to maximize the profit?
grams of caffeine and a cup of
tea has 20 grams of sugar and 25
toys, a cheetah toy and a cat toy. The
grams of caffeine. If the student
cheetah toy requires Tshs 2,000 for
drinks more than 100 grams of 9. A company makes two types of
sugar, he will suffer from diabetes materials and 4 hours of work. The cat
and shocks, and will fail his toy requires Tshs 3,000 for materials
78 Student\s Book Form Three
18/09/2025 09:59:15
MATHEMATIC F3 SB.indd 78
MATHEMATIC F3 SB.indd 78 18/09/2025 09:59:15
