DU SOL B.Com 2nd Year Business Mathematics and Statistics Set 1 Question Paper 2018 B-101 G-I

[This question paper contains 8 printed pages.]

1264 Your Rott No. ..............

B.Com. / II G_I

Paper Code : B-l0l

PApeT VI - BUSINESS MATHEMATICS AND STATISTICS
(Part A-Business Mathematics)

Time: I Hour Maximum Marks : 25

(IVrite your Roll |ttro. on the top immediately
on receipt of this question paper.)

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1264 2

l. The following matrtx grves the number
of units of three
hour on
products (P,, P, and Pr) that can be processed Per
three machines (M,, M, and Mr)

M' M. M3
l-- t2;ln'
lt, 11 20lP,
I t, 18 t4l
P,

many units of each
Determine by using matrix algebra' how
on machines
product can be produced, if the hours available
Mi, M2 and M, are 54, 46 and 48 respectively'
OR

Rs' 45000
A firm owns two machines M, and Mt costing
and Rs. 30000. Both machines have
five year lives with a
scrap value NIL. Calculate depreciation
of each machine
for each year using matrix notations when -

(i) Both are depreciated by Sum of the years digit method

(ii) Both bY Straight Line Method.
(iii) If first machine is depreciated bY sum of the Years
digit method and second bY straight fine method'
(7)

1264

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4
1264
glven
a particular product is
2. (a) The total cost in rupees for
by
x represents the
fC(x)=xi - 2lx2 +360x+3025' where
Determine
number of units produced'
unit'
(i) The marginal cost of the tenth
the marginal cost is
(ii) The uumber of units for which
minimum'

(iii) The minimum marginal cost'
cost for the number of units
Tl-re total cost and average
which minimizes the marginal cost'

OR

For the demand function
x=(u/p)-b ' verify that its
: R/(an-MR)'
price elasticity of demand

(b) A firm's price function
is P = 50iJX with the average
cost function AC(X)
: 0.50 + 1000/x. Find the price
and quantity where its
profit is maximum' Also find
maximised Profit'

OR

an item consists of Rs'
1000
The cost of manufacturing
Rs' 2 per unit and the labour
as overheads, material costs

t264 J

costs Rs. x2l90 for x units produced. Find the level of
output where per unit cost is minimum and the minimized
per unit cost.

(c) The rnarginal revenue function of a product is MR(X)
: l4l(2x+3)'l - l. Find the corresponding total revenue
function and the demand function.

OR

The marginal cost function of a product is MC(X) = 4 *
2x * x2. Find the corresponding total and average cost
functions if total cost at zero level is Rs. 100.
(4,4,4)

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1264 6

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d-Ir q.-i1-{ x + ftq =(ulp)*b, wsrfra dfrq fr fq fr
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1264 7

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3. (a) A machine costing Rs. 80,000 would reduce to
Rs.20,000 in 8 years. Find the rate of yearly
depreciation, given that depreciation is calculated using
diminishing balance method.

OR

State the relationship between nominal and effective
rate of interest (i) If compounding is n times in a year;
(ii) If compounding is continous.

(b) How much should be invested at 6o/a p.a. so that after
4 years the amount will be Rs. 25000 when the interest
is compounded (i) quarterly; (ii) Semi-annually.

OR

A sum of money is invested at 20%o p.a. for two years.
It would yield Rs. 482 more if interest were payable
semi-annually instead of annually. Find the sum.
(3,3)

1264 8

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(40,000)