Page 87 - Mathematics_Form_3

Linear programming
yield a profit of Tshs 250,000 and
Tshs 550,000 for P. How many
2
hectares of each plot should he 17. Ms. Matilda has three machines I,
cultivate to maximize profit? What
is the maximum profit?
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14. A school plans to buy goats. A
male goat costs Tshs 60,000 while
a female goat costs Tshs 75,000.
The school wants to buy not more
than 5 male goats. If it has prepared
to spend up to Tshs 1,200,000, find:
(a) The maximum number of
male and female goats the
school can buy.
(b) The maximum number of
goats the school can buy.
15. One kind of cake requires 100 g of
flour and 30 g of fat, and another
kind of cake requires 300 g of flour
and 20 g of fat. Find the maximum
number of cakes to be made from
6 kg of flour and 0.75 kg of fat
assuming that there is no shortage
of the other ingredients used in
Mathematics for Secondary Schools and F . Fertilizer F consists of 5%
making the cakes.
16. There are two types of fertilizers, F
1
2
1
nitrogen and 10% phosphoric acid
and F consists of 6% of nitrogen
2
and 5% of phosphoric acid. After
testing the soil conditions, a farmer
concludes that she needs at least
8.4 kg of nitrogen and 14 kg of
phosphoric acid for her crop. If F
1
costs Tshs 600 per kg and F costs 18. A farmer has 10 acres of land on
2
Tshs 500 per kg, how much of each
type of fertilizer should she use so
80
MATHEMATIC F3 SB.indd 80
MATHEMATIC F3 SB.indd 80
that the nutrient requirements are
met at minimum cost?
II, and III installed in her factory.
Machines I and II are capable of
being operated for at least 5 hours
a day, while machine III can operate
for not more than 14 hours a day.
She produces only two items M
and N each requiring the use of
all three machines. The number
of hours required for producing 1
unit of items M and N on the three
machines are given in the following
table:
Number of hours
Items required on machines
I II III
M 1 2 1
N 3 1 1
She makes a profit of Tshs 600
and Tshs 400 on items M and N,
respectively.
(b) Determine the maximum
(a) How many items of each type
should she produce so as to
maximize her profit, assuming
that she can sell all the items
that she produced?
profit.
which he can grow either mangoes
or oranges. She has 59 working
days available during cultivation
season. Mangoes require 5 days
Student\s Book Form Three
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18/09/2025 09:59:16