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Chapter 24 – Multicriteria Capital
Budgeting and Linear Programming
 Linear
programming is a mathematical
procedure, usually carried out by computer
software, to find an optimal combination to
maximize a goal function subject to
constraints.
Simple LP Problem
We cannot invest more than $3,000 in division 1 or more
than $2,000 in division 2. The amount invested in
division 1 must be at least twice as great as the amount
invested in division 2. x1 and x2 are the amounts
invested in divisions 1 and 2. The LP model is
Maximize
Subject to
.2x1+ .3x2
x1 ≤ $3,000
x2 ≤ $2,000
-x1 + 2x2 ≤ $0
x1 ≥ $0
x2 ≥ $0
Dual values
 Each
constraint has a dual value, which is
typically computed by the same software
that finds the original solution
 Dual values tells us how much the objective
function could be increased if we exceeded
a particular constraint by one unit
Sensitivity Analysis
 We
often solve a linear programming
problem several times, with constraints
changed. As a result of this analysis, we
might go back and look at ways to
overcome a particular constraint
Solving LP problems with Excel
 Excel
Solver can be used to solve LP
problems
 You may need to install Solver because it is
not automatically installed
Solver Illustration
Maximize
X1
X2
Sum
Limit
0.2
0.3
0
1
0
0
<=
3,000
0
1
0
<=
2,000
-1
2
0
<=
0
1
0
0
=>
0
0
1
0
=>
0
0
0
Subject to
Variable
values
Multiple Goals and Constraints
Managers can list multiple goals, such as NPV,
sales growth, EPS growth, etc.
 To put the goals in the objective function, each
must be given a weight
 Considerations can also be converted to
constraints. We might have a constraint that EPS
must increase at least 5% a year, for example

Capital rationing
 Set
the objective function as maximizing
wealth as of some specified future date,
given a fixed amount of capital available,
and specified infusions of capital each year,
if any.
 Must specify reinvestment opportunity rates
in future periods, at least in terms of
estimated external opportunity rates
Other Programming Techniques
 Integer
programming
 Goal programming
 Chance-constrained programming
 Quadratic programming