Table below shows the prices, the price indices and the proportion of four materials, A, B, C and D used in the production of a type of bag.
Material |
Price (RM) for the year |
Price index in the year 2014 based on the year 2011 |
Proportion |
|
2011 |
2014 |
|||
A |
x |
7.20 |
120 |
7 |
B |
8.00 |
9.20 |
115 |
3 |
C |
5.00 |
5.50 |
y |
6 |
D |
3.00 |
3.75 |
125 |
8 |
(a) Calculate the value of x and of y. [2 Marks]
(b) Find the composite index for the bag in the year 2014 based on the year 2011. [3 Marks]
(c) Given the cost for the production of the bag in the year 2014 is RM 115, find the corresponding cost in the year 2011. [2 Marks]
(d) From the year 2014 to year 2015, the price indices of material B and C increase by 5%, material A decrease by 10% and material D remains unchanged.
Calculate the composite index in the year 2015 based on the year 2011. [3 Marks]
Solution:
(a)
I=P1P0×100I=P2014P2011×100120=7.20x×100x=6.00y=5.505.00×100y=110
(b)
Composite index for bag in the year2014 based on the year 2011,ˉI=∑IW∑WˉI=(120)(7)+(115)(3)+(110)(6)+(125)(8)7+3+6+8ˉI=840+345+660+100024ˉI=118.54
(c)
ˉI=P2014P2011×100118.54=115P2011×100P2011=97.01
(d)
<Composite index for the bag in the year2015 based on the year 2011,ˉI=∑IW∑W=(120×0.9)(7)+(115×1.05)(3)+(110×1.05)(6)+100024=756+362.25+693+100024=117.14