EXERCISE 32D
1 4 litre cans of base white paint are converted into lime green or pine green by adding yellow tint and
blue tint in different proportions. For lime green we add 5 units of yellow tint to one unit of blue tint.
For pine green we add 1 unit of yellow tint to 4 units of blue tint.
If 15 units of yellow tint and 12 units of blue tint are available, state inequalities connectingx, the
number of cans of lime green paint that can be made, andy, the number of cans of pine green paint
that can be made.
2 An importer purchases two types of baseball helmet: standard helmets cost$80each and deluxe helmets
cost$120each. The importer wants to spend a maximum of$4800, and because of government
protection to local industry, can import no more than 50 helmets. Suppose the importer purchasesx
standard helmets andydeluxe helmets. List the constraints on the variablesxandy.
3 A farmer has a week in which to plant lettuces and cauliflowers. Lettuces can be planted at a rate of
8 ha per day and cauliflowers at a rate of 6 ha per day. 50 ha are available for planting.
Suppose the farmer plants lettuces forxdays and cauliflowers forydays. List, with reasons, the
constraints involvingxandy.
4 Two varieties of special food are used by athletes. Variety A
contains 30 units of carbohydrate, 30 units of protein, and 100
units of vitamins. Variety B contains 10 units of carbohydrate, 30
units of protein, and 200 units of vitamins. Each week an athlete
must consume at least 170 units of carbohydrate, at least 1400
units of vitamins, but no more than 330 units of protein.
a Let the number of tins of variety A bexand the number
of tins of variety B bey. Explain each of the constraints:
x> 0 ,y> 0 , 3 x+y> 17 ,x+y 611 andx+2y> 14.
b
c If variety A costs$ 5 per tin and variety B costs$ 3 per tin, find the combination which minimises
the cost.
d If the prices of tins change to$ 4 per tin for variety A and$ 9 for variety B, what combination
will now minimise the cost?56 A manufacturer produces two kinds of table-tennis sets:
Set A contains 2 bats and 3 balls, Set B contains 2 bats, 5 balls and 1 net.
In one hour the factory can produce at most 56 bats, 108 balls and 18 nets. Set A earns a profit of$3
and Set B earns a profit of$5.
a Summarise the information in a table assumingxsets of A andysets of B are made each hour.
b Write an expression for the total profit made$P.
c List the constraints.Graph the regionRdefined by these five inequalities.646 Inequalities (Chapter 32)A librarian has space for 20 new books. He needs to spend at leastE 240 to use his annual budget.
Hardback books costE 30 each and softback books costE 10 each.
If he buysxhardbacks andysoftbacks:
a explain why x> 0 , y> 0 , x+y 620 , and 3 x+y> 24.
b graph the region defined by the constraints.
c Use your region to find:
i the smallest number of books the librarian can buy
ii the largest amount of money the librarian can spend.IGCSE01
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_32\646IGCSE01_32.CDR Monday, 3 November 2008 9:31:28 AM PETER