Cambridge International Mathematics

a Copy and complete the table:

Meter Gears Dials Assembly time (min) Profit Number

Gas x

Water y

b Construct five constraints involvingxandy.

c

d Write an expression for the profit in terms ofxandy.

e How many of each meter need to be made to maximise the profit?

Review set 32B

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1 Use a graphics calculator to solve these inequalities:

a 2 x>

1

x

b x^4 +x 6 x^3 +x^2 +1

2

ab

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

x> 0 , y> 2 , x+y 65 , x+2y> 6 , 3 x+2y 612.

b List the points inafor which y=x+3.

c Which of the integer solutions inawould maximise the expression 5 x+4y?

4 A manufacturer makes 2 -drawer filing cabinets, and desks with a single drawer. The 2 -drawer

cabinet uses 1 lock and 3 square metres of metal, and yieldsE 34 profit. The desk uses 1 lock and

9 m^2 of metal, and yieldsE 47 profit. There are 14 drawers, 8 locks, and 54 square metres of metal

available. Find how many of each should be produced to earn the highest possible profit.

Graph the regionRdefined by the inequalities inb.

Write inequalities which completely specify these unshaded regionsR:

O

y

x

y¡=¡2

x¡=¡-2

R

O x

y

R

24

1

3

4

648 Inequalities (Chapter 32)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_32\648IGCSE01_32.CDR Friday, 31 October 2008 9:40:22 AM PETER