SUBJECT:- Quantitative Methods

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INDIAN SCHOOL OF BUSINESS

MANAGEMENT & ADMINISTRATION

AN ISO 9001 : 2008 CERTIFIED INSTITUTION

SUBJECT:- Quantitative Methods

MARKS :80

Course : MBA-4 Sem (Masters In Business Administration

Name :

Answer the question in one line.

 Q1. Differentiate the following with respect to x.

1. (x2+3)/(3x+1)

2. (ax+b)/(cx+d)

Answer:  1. Let

y=(x2+3)/(3x+1)

dy/dx=((3x+1).2x-(x2+3).3)/(3x+1)2

2. Let y=ax+b/cx+d

Q2. Find the Maximum and minimum values of x3-2x2+x+4.

Answer:  Let f(x)=x3-2x2+x+4

Df(x)/dx=3x2-4x+1

             =(x-1)(3x-1)

Q3. Find dy/dx of the following cases 1. y=x2 log x. 2. log x /x.

Answer:  

1. y=x2 log x.

2. log x /x.

Ans. 1. Y=x2logx

2. Let y=log x  /x

        

Q4. At what percent per annum will a sum of money double in 8 years?

Answer:  R=(n-1)*100/t

We know n=2

Q5. A revenue function is given by R= 35x-2x2 where R is the revenue and x is the quantity. What value of x maximizes revenue? What is the Maximum Revenue?

Answer:  R=35x-2x2

dR/dx=35-4x

for maxima or minima,

dR/dx=0

Q6. If a person deposits on a recurring deposit scheme, monthly Rs. 1500 for 4 years at 15% per annum, what would be thesum that can be received at the end of 4 years.

Answer:  T=4

R=15%

Q7. An insurance company allows interest at 10% p.a., compounded annually. What initial payment will enable a person to purchase perpetuity of Rs.1500 per annum?

Answer:  C.I=P(1+(1-R/100)n)

1500=P(1+(1-10/100)1)

Q8. What is a linear programming problem? Discuss the scope and role of linear programming in solving managementproblems. Discuss and describe the role of linear programming in managerial decision-making bringing out limitations, if any.

Answer:  linear programming problemàLinear Programming (LP) is a mathematical technique designed to help managers in their planning and decision-making. It is usually used in an organisation that is trying to make the most effective use of its resources. Resources typically include machinery, manpower, money, time, warehouse space, and raw materials. A few examples of problems in which LP has been successfully applied are:

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