# Arpit Kothari Essay

862 words - 4 pages

QUANTITATIVE ANALYSIS FOR BUSINESS 1 ASSIGNMENT 2
QUESTION 1
a) Suppose the monthly revenue and cost functions (in dollars) for
commodity produced and sold are:

( ) = 400 −

and

units of a

( ) = 5000 + 70

respectively.
i)

Find the profit function.
Solution:

[2 marks]

Revenue function R(x) = 400 −

20

Cost function C(x) = 5000 + 70
Profit Function is defined as

( )= ( )− ( )

= 400 −
( ) = 330 −

ii)

− 5000

Find the marginal profit function.
[2 marks]
Solution:
Marginal profit is the difference between the marginal revenue & marginal
cost of producing one additional unit of output.
i.e., m( ) = ( ) − ( ) = ( )
=>

iii)

−500 − 70

.=

. .

. . = . .∗

where T.R.=Total Revenue & Q= Quantity
= 54

+ 13

− 12

Find:
ii)

The total revenue if 100 units were sold.
Solution:
For 100 units,
. . = 54(100) + 13(100) − 12(100)
= 100(540000 + 1300 + 12)
= 54128800 (
)

iii)

The revenue attributable to the sale of the 81st unit, using the marginal
approach.
[4 marks]
Solution:
Marginal Revenue (M.R.) =
. . ( ) = 162

[2 marks]

( . .)

+ 26 − 12

Therefore, revenue attributable to the sale of 81st unit will be. . (81) = 162(81) + 26(81) − 12
= 15216 (
)

b) A firm has determined that its weekly profit function is given by:
( ) = 95 − 0.05 − 5000 for 0 ≤ ≤ 1000. Find the volume of production that
maximises profit.
[2 marks]
Solution:
( ) = 95 − 0.05 − 5000 ; 0 ≤ ≤ 1000
For Maximum profit, Marginal profit should be equal to zero.
i.e., ( ) = 0
=> 95 − 0.1 = 0
=> = 950
Hence, for maximum profit, 950 units of goods should be manufactured.

QUESTION 3
The following is a table of revenue (in \$) and quantities of a certain commodity.
RAW
MATERIAL

QUANTITIES

1997
1300
2200
2000
1200
1150

I
II
III
IV
V

TOTAL REVENUE (\$)

1997
50
40
30
20
10

1998
1000
1500
1200
1600
1150

1998
60
50
40
30
20

Calculate:
a) The Price Relative for Raw Material V.
Solution:
Taking base year as 1997(

[2 marks]

1150
1998
1
= 20 = = 0.5
1997 1150 2
10

)=

b) The Quantity Relative for Raw Material II.
Solution:
(

)=

[2 marks]
1998 50 5
=
= = 1.25
1997 40 4

c) The Unweighted Aggregative Price Index.
Solution:

;
Unweighted Price Index =

Where, Pn = current prices, Po = base year prices

RAW
MATERIAL

I
II
III
IV
V

TOTAL
REVENUE
(\$)
1997 1998
1300 1000
2200 1500
2000 1200
1200 1600
1150 1150
TOTAL

QUANTITIES

1997
50
40
30
20
10

1998...

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