Question

In: Operations Management

3. (20 pts) Hilton Financial Inc. has just obtained $240,000 for investment and would like to...

3. (20 pts) Hilton Financial Inc. has just obtained $240,000 for investment and would like to maximize investment return. The firm’s top financial analyst recommends that all new investments be made in the automobile industry (Ford, Honda), retail industry (Target, Wal-Mart), or in government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of return:

Investment Projected Rate of Return

Ford 12%

Honda 11%

Target 8%

Wal-Mart 6%

Government Bonds 5%

Management of Hilton imposed the following guidelines:

1. Neither industry (automobile or retail) should receive more than $140,000.

2. Government bonds should be at least 25% of the retail industry investments.

3. The investment in Ford can not be more than 65% of the total automobile industry investment.

The investment in Target may not exceed 70% of the investment in Wal-Mart.

5. No more than 60% of the total funds invested in stock (automobile and retail) may be invested in the automobile industry, and no more than 55% of the funds invested in stock (automobile and retail) may be invested in the retail industry.

Formulate a linear programming model of the problem to find out how much to invest in each security.

3. (20 pts) Hilton Financial Inc. has just obtained $240,000 for investment and would like to maximize investment return. The firm’s top financial analyst recommends that all new investments be made in the automobile industry (Ford, Honda), retail industry (Target, Wal-Mart), or in government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of return:

Investment Projected Rate of Return

Ford 12%

Honda 11%

Target 8%

Wal-Mart 6%

Government Bonds 5%

Management of Hilton imposed the following guidelines:

1. Neither industry (automobile or retail) should receive more than $140,000.

2. Government bonds should be at least 25% of the retail industry investments.

3. The investment in Ford can not be more than 65% of the total automobile industry investment.

The investment in Target may not exceed 70% of the investment in Wal-Mart.

5. No more than 60% of the total funds invested in stock (automobile and retail) may be invested in the automobile industry, and no more than 55% of the funds invested in stock (automobile and retail) may be invested in the retail industry.

Formulate a linear programming model of the problem to find out how much to invest in each security.

Expert Solution

Answer: We will formulate LP model for the given problem as mentioned below;

Decision Variables:

Let Decision Variables:

x1 = $ Amount to be invested in the stock of Ford,

x2 = $ Amount to be invested in the stock of Honda,

x3 = $ Amount to be invested in the stock of Target,

x4 = $ Amount to be invested in the stock of Wall-Mart, and

x5= $ Amount to be invested in Government Bond

Where x1 + x2 = Total investment in automobile industry, and x3 + x4 = Total investment in retail industry

Objective Function:

Here, the main objective is to maximize the total return, hence the objective function =

0.12 x1 + 0.11 x2 + 0.08 x3 + 0.06 x4 + 0.05 x5

Subject to Constraints:
C1 = x1 + x2 + x3 + x4 + x6 ≤ 240000 (Total amount to be invested)

C2 = x1 + x2 ≤ 140000 (Max. amount to be invested in automobile industry)

C3 = x3 + x4 ≤ 140000 (Max. amount to be invested in retail industry)

C4 = x5 ≥ 0.25 ( x3 + x4) (Investment in Gov. Bonds should be at least 25% of total retail industry investiment)

C5 = x1 ≤ 0.65 ( x1 + x2) (Investment in Ford can not be more than 65% of the total automobile industry investment)

C6 = x3 ≤ 0.70 x4 (Investment in Target may not exceed 70% of the investment in Wal-Mart)

C7 = x1 + x2 ≤ 0.60 ( x1 + x2 + x3 + x4) [No more than 60% of the total funds invested in automobile and retail retail industry may be invested in the automobile industry]

C8 = c3 + c4 ≤ 0.55 ( x1 + x2 + x3 + x4) [No more than 55% of the funds invested in stock (automobile and retail) may be invested in the retail industry]

Non-Negativity Condition:

x1, x2, x3, x4, x5 ≥ 0

[Note: As no specific information is mentioned in the question we will just formulate an LP model. (No need to solve) ]

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