Transcript UNIVERSITY MALAYA FAKULTI PERNIAGAAN & PERAKAUNAN

UNIVERSITI MALAYA
FAKULTI PERNIAGAAN & PERAKAUNAN
CBEB 1110 : QUANTITATIVE ANALYSIS
FOR BUSINESS
WEEK 12: QUESTION & ANSWERS
QUESTION 1
A firm’s demand function is given by
P = 100 - 4Q ½ - 3Q
(a) Write down an expression for total revenue, TR, in terms of Q.
(b) Find an expression for the marginal revenue, MR, and find the
value of MR when Q = 9
(c) Use the result of part (b) to estimate the change in TR when Q
increases by 0.5 unit and compare this with the exact change in TR.
QUESTION 2
A manufacturer has fixed costs of $200 each week, and the variable costs
per unit can be expressed by the function, VC = 2Q − 36
(a) Find an expression for the total cost function and deduce that the average
cost function is given by AC  200  2Q  36
Q
(b) Find the stationary point of this function and show that this is a minimum.
(c) Verify that, at this stationary point, average cost is the same as marginal cost
QUESTION 3
An advertising agency spends $x on a newspaper campaign and a further $y
promoting its client’s products on local radio. It receives 15% commission on
all sales that the client receives. The agency has $10 000 to spend in total,
and the client earns $M from its sales, where;
10000 x 40000 y
AC 

50  x
30  y
Use the method of Lagrange multipliers to determine how much should be
spent on advertising in newspapers and on radio to maximize the agency’s
net income. Give your answers correct to two decimal places.
Answer 3
QUESTION 4
Use Lagrange multipliers to find the maximum utility for the utility
function U = 5xy, when subject to a budget of RM 30, where the price
of each unit of X is RM5 and each unit of Y is RM1
QUESTION 5
There are 50 apple trees in an orchard. Each tree produces 800 apples.
For each additional tree planted in the orchard, the output per tree drops
by 10 apples. How many trees should be added to the existing orchard
in order to maximize the total output of trees?
QUESTION 6
The following is given for a product of a company
Marginal cost : RM(20+0.2x) where x is the quantity sold . Fixed cost
is RM 500. Demand function is linear:
At price of RM 78, 30 units are sold.
At price of RM 58, 50 units are sold.
Find:
a)
The demand function
b)
The total cost function
c)
The total revenue function
d)
Level of production which maximize profit
e)
Maximum profit, price per unit, total revenue and total cost when
profit is maximized
f)
The level of production in which total revenue is maximized
g)
The profit, price per unit, total revenue and total cost when total
revenue is maximized
a) The demand function
b) Total cost function
c) The total revenue function
d) Level of production at max profit
e)
f)
g)
QUESTION 7
Sebuah syarikat penyiaran sedang giat melancarkan kempen
menambah bilangan pendengarnya. Pada masa kini jumlah
pendengarnya adalah sejumlah 27,000 orang tiap hari. Pihak
pengurusan mengenal pasti bilangan pendengar (S) ini akan
bertambah pada kadar : S ( x)  60t 1/ 2
Di mana t merupakan bilangan hari kempen in berlangsung. Tentukan
bilangan hari kempen ini perlu diteruskan bagi memastikan bilangan
pendengar bertambah ke angka 41,000 orang.
THE END