Page 86 - Mathematics_Form_3

Linear programming
and 4 hours of work. The company
has Tshs 44,000 for materials and
72 hours of work to make at least 7
toys of each type. Find the number
of toys of each type the company
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should make to maximize the profit
if each cheetah and cat toy makes
a profit of Tshs 16,000 and Tshs 12. A poultry farmer intends to sell his
12,000, respectively. What is the
maximum profit?
10. Two friends are planning an
exercise program to keep their
bodies fit. They want to spend up
to 1.5 hours per day on aerobics
and flexibility exercises. They
prefer aerobics than flexibility,
but can not manage more than 60
minutes of aerobics. They know
that aerobics use 8 calories per
minute and flexibility exercises use
3 calories per minute. They wish
to lose the maximum number of
calories. How should the planning
program be done in order to have
maximum loss of calories? What
is the maximum losses of calories?
11. A special diet for laboratory animals
is to contain at least 300 units of
vitamins, 110 units of minerals, and
240 calories. There are two mixtures,
A and B of diet available. One gram
of mixture A contains 3 units of
vitamins, 1 unit of minerals, and
2 calories. One gram of mixture B
contains 2 units of vitamins, 1 unit of
minerals, and 4 calories. Mixture A
costs Tshs 400 per gram and mixture
B costs Tshs 600 per gram.
Student\s Book Form Three 79
MATHEMATIC F3 SB.indd 79
MATHEMATIC F3 SB.indd 79
(a) How many grams of each
mixture should be used to
satisfy the requirements of the
diet at a minimum cost?
(b) Find the cost of the cheapest
diet.
chicken and ducks. After visiting
the market, he formulated a linear
programming problem as follows.
Let x be the number of chicken to
be sold and y be the number of
ducks to be sold.
Maximize ( , ) 8500f xy = x + 12500y.
max
Subjected to:
x +≤ 7
y
x + 2y ≤ 8
x ≥ 2y
x ≥ 0
y ≥ 0
(a) Solve the linear programming
problem graphically.
(b) Determine the optimal value
for maximization of profit.
13. A farmer has two plots of land P
1
and P. . Plot P requires 2 kg of
2
1
maize seeds and 1 kg of millet seeds
per hectare. Plot P. requires 1 kg Mathematics for Secondary Schools
2
of maize seeds and 4 kg of millet
seeds per hectare. He can cultivate
at most 9 hectares of maize and at
least 1 hectare of millet. He can
purchase not more than 20 kg and
30 kg of maize and millet seeds,
respectively. Each hectare of P
1
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