Cambridge International Mathematics

d Determine how many of each set the manufacturer should make each hour to maximise the profit.

e Are any components under-utilised when the maximum profit is achieved?

7 A manufacturer of wheelbarrows makes two models, Deluxe

and Standard.

For the Deluxe model he needs machine A for 2 minutes

and machine B for 2 minutes.

For the Standard model he needs machine A for 3 minutes

and machine B for 1 minute.

Machine A is available for at most 48 minutes and machine

B for 20 minutes every hour.

He knows from past experience that he will sell at least twice as many of the Standard model as the

Deluxe model. The Deluxe model earns him$ 25 profit and the Standard model earns$ 20 profit.

a Construct a set of constraints ifxDeluxe models andyStandard models are made.

b Write an expression for the profit$Pin terms ofxandy.

c Graph the region defined by the constraint inequalities.

d How many of each model should be made per hour in order to maximise the profits?

Review set 32A

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1 Use a graphics calculator to solve these inequalities:

a x^2 +4x¡ 1 > 0 b x^3 +11x< 6 x^2 +5

2

ab

3aFind all points with integer coordinates which lie in the region defined by:

x> 2 , y> 1 ,x+y 67 , x+y> 5 , 2 x+y 610.

b If the constraint x> 2 changes to x> 2 , what effect does this have on your answers ina?

5 A factory makes gas meters and water meters. Gas meters need 4 gears, 1 dial, and 8 minutes of

assembly time for a profit of$20. Water meters need 12 gears, 1 dial, and 4 minutes of assembly

time for a profit of$31. There are 60 gears, 9 dials, and 64 minutes of assembly time available for

use in this production.

Write inequalities which completely specify these unshaded regionsR:

O

y

x

R

2

3

36

O

y

x

R

y¡=¡-3

x¡=¡2

Inequalities (Chapter 32) 647

4aGraph the regionRdefined by the inequalities: x> 0 , y> 0 , x+y> 12 , x+2y> 16.

b Find all points(x,y)inRwith integer coordinates such that x+y=14.

c Find the minimum value of 3 x+2y for all points inRwherexandyare integers.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_32\647IGCSE01_32.CDR Friday, 31 October 2008 9:38:37 AM PETER