practice problems1

# practice problems1 - Deterministic Math Models(550.251...

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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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practice problems1 - Deterministic Math Models(550.251...

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