Page 82 - Mathematics_Form_3

Linear programming

X and Tshs 21,430 for product Y. has 48 hired labourers available.
Solve this problem graphically to To maintain one hectare of coffee
obtain the maximum contribution he needs 250,000 shillings while
of each product. one hectare of potatoes costs him

9. A wheat and barley farmer has 168 100,000 shillings. Find the largest
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hectare of ploughed land, and a capital possible area of land he can sow
of Tshs 4,000,000. It costs Tshs 28,000 if he is prepared to use 2,500,000
to sow one hectare of wheat and shillings.
Tshs 20,000 to sow one hectare of 11. A technical school is planning to
barley. Suppose that his profit is Tshs buy two types of machines. A lather
160,000 per hectare of wheat and machine needs 3 m of floor space
2
Tshs 110,000 per hectare of barley. and a drilling machine requires
Use the graphical method to find the 2 m of floor space. The total space
2
optimal number of hectares of wheat available is 30 m . The cost of one
2
and barley that must be ploughed in lather machine is 250,000 shillings,
order to maximize profit. a drilling machine costs 300,000

10. A farmer wants to plant coffee shillings. The school can spend not
and potatoes. Coffee requires 3 more than 3,000,000 shillings. Find
persons per hectare and potatoes the greatest number of machines the
require 3 persons per hectare. He school can buy.

12. Wheat and maize are to be planted on a farm, subject to the following constraints.

Wheat Maize Maximum total
Labour days per hectare 2 1 10

Labour cost per hectare (Tshs) 30,000 60,000 300,000
Cost of fertilizer per hectare (Tshs) 40,000 40,000 240,000

(a) Find the largest area that can be planted.
(b) If wheat yields a profit of 80,000 shillings per hectare while maize Mathematics for Secondary Schools

yields 60,000 shillings per hectare, how should the area be planted?
13. A manufacturing company has two plants which produce three types of
products namely SMALL, MEDIUM, and LARGE products. The first plant
can manufacture 3 units of the SMALL product, 12 units of the MEDIUM
product, and 12 units of the LARGE product at a cost of 24,000 shillings
per hour. The second plant can manufacture 9 units of the SMALL product,
15 units of the MEDIUM product, and 3 units of the LARGE product at

Student\s Book Form Three 75

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MATHEMATIC F3 SB.indd 75