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Deterministic Math Models (550.251)
Practice Problems: Multivariable Nonlinear Optimization
General Directions:
You must show all work and document any assumptions to receive
full credit. All problems are to be done by hand unless otherwise stated.
1. An investor has $2 million to invest. He has 5 opportunities for investment, with the
following characteristics:
i) The yield on the ﬁrst investment is given by a linear function:
r
1
= 3 + 0
.
000012
x
1
,
where
r
1
= yield per year (%), and
x
1
= amount invested ($).
Minimum required: $100,000
Maximum allowed: $1,000,000
Years to maturity: 6
ii) The second investment yields:
r
2
= 2 + 0
.
000018
x
2
,
where
r
2
= yield per year (%), and
x
2
= amount invested ($).
Minimum required: $200,000
Maximum allowed: $1,000,000
Years to maturity: 10
iii) An investment at 5% per year with interest continuously compounded. (An amount
A
invested at 5% per year with continuously compounded interest becomes
Ae
0
.
05
after
one year.) Years to maturity: 1

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