MATHEMATICS
Textbook for Class XII
PART I
MATHEMATICS
Textbook for Class XII
PART I
Foreword
The National Curriculum Framework, 2005, recommends that childrens life at school
must be linked to their life outside the school. This principle marks a departur
Ambulance Service Problem
Gotham City Ambulance Service
Gotham city is divided into 8 districts, each with a
population (in 1000s) as given in the Table below:
Districts
Population (in 1000s)
1
40
2
30
3
35
4
20
5
15
6
50
7
45
8
60
Gotham City Ambulance
Using Excel Functions
Rand Function
In Excel, the Rand function is used to return a random number that is greater
than or equal to 0 and less than 1. It returns a new random number each time
your spreadsheet recalculates.
The syntax for the random number
Answers to numericals among Problems at the end of Chapter 1:
1.1
Part c: Mix is 6399 liters Regular and 1528 liters premium
Part d: Mix is 0 liters Regular and 6182 liters premium
Comparison: In part c, contribution was Rs.1190664 and employees got Rs.44
Kowloon Development Co. Ltd.
Decision Analysis
2016 17 Session
Defining a solution to the problem
Do we buy the plot or put money in the bank?
Do we apply for increasing development ratio if we buy it?
Do we construct on the plot if we buy it?
Unreason
Sarah Changs Dilemma
Decision Analysis
2016 17 Session
What is a solution to the problem?
Does Sarah invest $200K in R&D or not?
If Sarah has the old technology only, should she bid or not?
If Sarah has the new technology and old technology, what shoul
The FACET problem
Decision Analysis
2016 17 Session
The nature of the problem
New product (which is not an
extension of an existing
product).
Decision to stock FACETs have
already been taken. The
question is how many?
Stocking in multiples of 100
piece
Applications of mathematical programming
Decision Analysis
2016 17 Session
Allocating trainees to departments
ASSEMBLY LINE
MACHINE SHOP
SYSTEMS
BACK OFFICE
ASSEMBLY LINE 1
ASSEMBLY LINE 2
MACHINE SHOP 1
MACHINE SHOP 2
SYSTEMS
BACK OFFICE
Assignment probl
Market
Research
Result
Production Process
Prototype for Phase 1
Phase 1 Market research result
Small Run (Phase 1)
Prototype for Phase 2
Phase 2 Market research result
Small Run (Phase 2)
Commercialization
NPV of Total Production Cost
Product goes to mark
Merton Trucks
Problem formulation - Conceptual
What is Merton deciding?
What constrains Mertons choices?
What options are available at hand?
Sales Manager: Stop manufacturing Model 101.
Controller: Increase Model 101, cut back on Model 102.
Production
Duality Theory
Ankur Sinha, PhD
Production and Quantitative Methods
Indian Institute of Management Ahmedabad
Gujarat India
Resouce Allocation vs Resource Valuation
Until now the problems that we considered were resource
allocation (primal) problems
Corr
Balance Sheet
Part 2
Prepare a Balance Sheet as on 30 March 2010,
using the following information [p: 44 - TEXT]
Cash
89000 Capital
1000000
Accounts Payables
241000 Premises
1120000
Machinery
761000 Bonds payable
700000
Estimated tax liability
125000 Accu
Balance Sheet
MANAC I
Session 2
What are the outputs of an
Accounting?
Financial Statements:
Balance Sheet
Profit and Loss Account
Basic Concepts to be known:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Money measurement.
Entity.
Going concern.
Cost.
D
Module III
Understanding of Financial
Statements
WHAT IS AN ACCOUNTING?
Sources of information
Annual Reports
Quarterly reports
Prospectus
Others
2
What does an Annual Report
consists of
Write down the list of items that you find in an
Annual Report?
3
Prepare a Balance Sheet as of 30
March 2010, for the SK Company,
using the following information
Cash
89000 Capital
1000000
Accounts Payables
241000 Premises
1120000
Machinery
761000 Bonds payable
700000
Estimated tax liability
125000 Accumulated deprecia
Cash Flow Statement
MANAC I
Transactions
ASSETS
Liabiliti
es
CC
a
Invested cash in business
b
Paid rental expenses
c
Received professional fees in cash
d
Bought supplies for cash
e
Bought equipment on credit
f
Withdrew cash
g
Bought suplies on account
h
L
Conditional inclusion of constraints
Decision Analysis
2016 17 Session
Choosing of options
Suppose you have n projects and must choose at most k of them to pursue. (Each project has a cost,
and you have a budget ) How would you model this decision problem
Integer Programming
Introduction
Until now we have looked at linear problems with continuous decision variables
A number of real-world situations involve decision variables that are integers, for
instance
Pure Integer Variables
There are two kinds of air
Worker Scheduling
Worker scheduling model
A post office requires different numbers of full-time employees
on different days of the week.
Day of Week
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Min. no. of Workers Required
17
13
15
19
14
16
1
Dharwar Prime Drilling Society
Without DPDS
Apply for loan
Bank
Receive loan
Start digging
Farmer
Govt.
Without DPDS
Apply for loan
Bank
Receive loan
Repay liability
Stop digging
Apply for subsidy
Govt.
Farmer
Receive subsidy
Without DPDS
Apply for loan
B