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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