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FINANCIAL APPLICATIONS 171
Table 4.14 Investment Opportunities for Welte Mutual Funds
Investment Projected Rate of Return (%)
Atlantic Oil 7.3
Pacific Oil 10.3
Midwest Steel 6.4
Huber Steel 7.5
Government bonds 4.5
What portfolio recommendations – investments and amounts – should be made for
the available E100 000? Given the objective of maximizing projected return subject
to the budgetary and managerially imposed constraints, we can answer this question
by formulating and solving a linear programming model of the problem. The
solution will provide investment recommendations for the management of Welte
Mutual Funds.
Let:
A ¼ euros invested in Atlantic Oil
P ¼ euros invested in Pacific Oil
M ¼ euros invested in Midwest Steel
H ¼ euros invested in Huber Steel
G ¼ euros invested in government bonds
Using the projected rates of return shown in Table 4.14, we write the objective
function for maximizing the total return for the portfolio as:
Max 0:073A þ 0:103P þ 0:064M þ 0:075H þ 0:045G
The constraint specifying investment of the available E100 000 is:
A þ P þ M þ H þ G ¼ 100 000
The requirements that neither the oil nor the steel industry should receive more
than E50 000 are:
A þ P 50 000
M þ H 50 000
The requirement that government bonds be at least 25 per cent of the steel industry
investment is expressed as:
G 0:25ðM þ HÞ or 0:25M 0:25H þ G 0
Finally, the constraint that Pacific Oil cannot be more than 60 per cent of the total
oil industry investment is:
P 0:60ðAþPÞ or 0:60Aþ0:40P 0
By adding the nonnegativity restrictions, we obtain the complete linear program-
ming model for the Welte Mutual investment problem:
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