Question

Problem It An investor has $1,000,000 to invest at the start of year I. He can invest in five different bach fund has different availability and maturity times as shown in the table below. As an sen dollr invested in fund A at the beginning of year I returns 50.50 at the start of year 2 and at the start of year 3, Similarly, each dollar invested in fund B in year 2 yields $1.25 at the start of year 4 (a Additionally, any money on earn 8% interest th dashindicates that no money can move in our out of a fund in a given year) hand and not placed into an investment at the start of a particular year will at year. The investor wants to keep at least $50,000 on hand at the start of each year to maximize the amount of money on hand at the start of year a nvest no more than $500,000 in any single fund. Formulate a linear program to enable him und Year 4 ear 2 0.5 Year 3 0.8 CHr 1,25 1.35 1.13 1:27 Objectrve moimd fruemari nize amounty mendy on Ahand at the steute

Answer 1

Linear program is following:

Decision variables: Let A, B, C, D, E be the amount to be invested in respective fund

FI be the amount of money on hand at start of year i

Objective function: Max F4

Constraints:

A+C+E+F1 = 1000000

0.5A + 1.08F1 - B - F2 = 0

0.8A + 1.27E + 1.08F2 - D - F3 = 0

1.25B + 1.35C + 1.13D + 1.08F3 - F4 = 0

A, B, C, D, E <= 500000

F1, F2, F3, F4, F5 >= 50000

A, B, C, D, E, F1, F2, F3, F4 >= 0