**Thank You!**

Our Optimal Solution

{Z= 1.118, G =.311, I = .2, M = .4889}

Original LP model:

max P = (1.18G + 1.125I + 1.075M)x

such that

G + I + M ≤ 1

(.10)G + (.07)I + (.01)M ≤ .05.

.20 ≤ G ≤ .40

.20 ≤ I ≤ .50

.30 ≤ M

Client's Concern about Growth Fund

Not too much money in growth fund

Let us invest your money...

Investment amount: $500

Maximum Risk Tolerance: .05

First Year Yield:

$559.00

Fifth Year Yield:

$976.34

**By: Adam Coppock, Greg Yerkes, Sunny Mitra**

**Investment Strategies**

G + I + M ≤ 1

(.10) G + (.07) I + (.01) M ≤ .05

.20 ≤ G ≤ .40

.20 ≤ I ≤ .50

.30 ≤ M

Task:

Design a Linear Programming model for J.D. Williams Inc.

Help maximize the yields of their clients’ financial portfolios.

J.D. Williams Inc.

Investment Advisory firm

Asset-Allocation Model:

Invests clients money into multiple funds

Three Types of Funds

Growth Fund

Main goal of capital appreciation

Has little to no dividend payout for the investor

Requires the highest tolerance for risk

Associated risk:

.10

Annual yield:

18%

Income Fund

Primary focus on the current income

Income made at varying intervals (monthly, annually, etc.)

Associated risk:

.07

Annual yield:

12.5%

Money-Market Funds

similar to a saving account

returns higher interest rates

Manages more than $120 million

Meet our investor:

Would like to invest:

$800,000

Maximum risk tolerance:

.05

Associated risk:

.01

Annual yield:

7.5%

Objective Function:

G

= Percentage invested in growth funds

I

= Percentage invested in income funds

M

= Percentage invested in money market funds

Maximize p = (1.18 G + 1.125 I + 1.075 M) x

Constraints:

$248,800 into growth funds

$160,000 into income funds

$391,200 into money-market funds

Re-assessing Risk Index

(.10)G+(.07)I+(.01)M ≤

.055

{Z= 1.118, G =.311, I = .2, M = .4889}

○ $293,360 into growth funds

○ $160,000 into income funds

○ $346,640 into money-market funds

Annual Yield: $899,200

Revision of Yield from Growth Fund

Yield of 16%

Yield of 14%

max Z =

( )

G + 1.125 I + 1.075 M

{Z= 1.111, G =.31, I = .2, M = .49}

○ $248,800 into growth funds

○ $160,000 into income funds

○ $391,200 into money-market funds

{Z= 1.106, G =.30, I = .3667, M = .4333}

○ $160,000 into growth funds

○ $293,360 into income funds

○ $346,640 into money-market fund

Annual Yield: $884,800

$213,360 into growth funds

$213,360 into income funds, and

$373,280 into money-market funds

Annual Yield: $888,800

Annual Yield: $894,400

Annual Yield: $892,800

G ≤ I

Revising the Yields

One at a Time

All Together

The optimal distribution of investment remains the same when:

Growth Fund:

Yield > 15%

Income Fund:

Yield < 14.5%

Money Market Fund:

1.5% < Yield < 18%

g

= Annual yield for growth fund

i

= Annual yield for income fund

m

= Annual yield for money market fund

Multiple conditions due to free variables,

some can be eliminated subject to

g

,

i

,

m

>1

m

is minimum

Binding condition:

g <= 10m

i <= 0.67 g + 0.33 m

m > 0

Modifying to Suit Every Client

The optimal basic feasible set remains the same under the following condition:

(not necessarily the same optimal investment distribution)

0.04 < Risk Index < 0.058

Modified LP model:

max Z = 1.18G + 1.125I + 1.075M

such that

G + I + M ≤ 1

(.10)G + (.07)I + (.01)M ≤ .05.

.20 ≤ G ≤ .40

.20 ≤ I ≤ .50

.30 ≤ M