Page 88 - Mathematics_Form_3

Linear programming

of labour per acre while oranges hour in the finishing department
require 8 days of labour per acre. and 2 hours in the painting
The net profit from mangoes department. The maximum number
per acre is 300,000 Tanzanian of hours available in the finishing
shillings per acre and for oranges and painting departments is 6 and
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it is 450,000 Tanzanian shillings 8, respectively. Machine A must
per acre. How many acres of each produce at least 2 items, while
crop should she plant to maximize machine B must produce at least
her profit? What is the maximum one item.
profit? (a) If the items produced on

19. A factory has two machines A and machine A give a profit of Tshs.
B which produce different items. 550,000 and Tshs. 450,000 for
An item produced on machine machine B, what is the optimal
A takes 1 hour in the finishing solution for maximisation of
department and 1 hour in the profit?
painting department. An item (b) What is the maximum profit?
produced in machine B takes 1

20. A poultry farmer wishes to produce a chicken feed which is a blend of two
inputs labelled P and Q. Each unit of input P and Q costs Tshs 4000 and Tshs
1000, respectively. The following table shows the percentage of ingredients
in each blend input and the minimum daily requirements:

Proportion of input Minimum
per unit of blend (%)
Ingredients requirements
(grams)
P Q
Protein 15 60 180
Carbohydrates 10 10 50
Salt 15 30 120 Mathematics for Secondary Schools
How can the farmer produce a chicken feed which meets the minimum
requirements at the least cost?

Student\s Book Form Three 81

18/09/2025 09:59:16
MATHEMATIC F3 SB.indd 81
MATHEMATIC F3 SB.indd 81 18/09/2025 09:59:16