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:

r1 = 3 + 0.000012x1,

where r1 = yield per year (%), and x1 = amount invested ($).

Minimum required: $ 100,000

Maximum allowed: $1,000,000

Years to maturity: 6

ii) The second investment yields:

r2 = 2 + 0.000018x2,

where r2 = yield per year (%), and x2 = 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 Ae0.05 after one year.

) Years to maturity: 1

iv) Category 1 of government bonds that yield 6% per year.

Years to maturity: 4

v) Category 2 of government bonds that yield 5.5% per year.

Years to maturity: 3

The average years to maturity of the entire portfolio must not exceed 5 years.

a) The objective of the investor is to maximize accumulated earnings at the end of the first year. Formulate a model to determine the amounts to invest in each of the alternatives. Assume all investments are held to maturity.

b) Identify the special type of nonlinear program obtained in part (a).