Question

An investor has money-making activities A and B available at the beginning of each of the next 5 years (call them years 1 to 5). Each dollar invested in A at the beginning of 1 year returns $1.40 (a profit of $0.40) 2 years later (in time for immediate reinvestment). Each dollar invested in B at the beginning of 1 year returns $1.70 3 years later.

In addition, money-making activities C and D will each be available at one time in the future. Each dollar investment in C at the beginning of year 2 returns $1.90 at the end of year 5. Each dollar invested in D at the beginning of year 5 returns $1.30 at the end of year 5.
The investor begins with $50,000 and wishes to know which investment plan maximizes the amount of money that can be accumulated by the beginning of year 6. Formulate the linear programming model for this problem.

Answer 1

Linear programming model is 1.90 C2 + 1.70 B3 + 1.40 A4 + 1.30 D5

Step-by-step explanation:

a. Decision Variables:

At = Money invested to A in t years ---- (t = 1,2,3,4)

Bt = Money invested to B t years ---- (t = 1,2,3)

C2 = Money invested to C in year 2 ----

D5 = Money invested to C in year 2 ----

R2 = Money not invested in t years ---- (t = 1,2,3,4)

b. Constraints

i) Equalities year wise

A1 + B1 +R1 = 50000 -------> Year 1

A2 + B2 +R2 = R1 -------> Year 2

A3 + B3 +R3 = 1.4 A1 + R2 -------> Year 3

A4 + R4 = 1.4 A2 + 1.7 B1 + R3 -------> Year 4

D5 = 1.4 A2 + 1.7 B2 + R4 -------> Year 5

ii) Non- Negative Constraints

At > 0 for t = 1,2,3,4

Bt > 0 for t = 1,2,3

C2 > 0

D5 > 0

Rt > 0 for t = 1,2,3,4

iii) Objective function will be = 1.90 C2 + 1.70 B3 + 1.40 A4 + 1.30 D5