Question

Information on a prospective investment for Wells Financial Services is given below. Period 1 2 3 4 Loan Funds Available 3000 7000 4000 5000 Investment Income (% of previous period's investment) 110% 112% 113% Maximum Investment 4500 8000 6000 7500 Payroll Payment 100 120 150 100 In each period, funds available for investment come from two sources: loan funds and income from the previous period's investment. Expenses, or cash outflows, in each period must include repayment of the previous period's loan plus 8.5% interest, and the current payroll payment. In addition, to end the planning horizon, investment income from period 4 (at 110% of the investment) must be sufficient to cover the loan plus interest from period 4. The difference in these two quantities represents net income, and is to be maximized. How much should be borrowed and how much should be invested each period?

Answer 1

Answer:

Let Lt = Loan in period t , t= 1...4

It = Investment in period t, t= 1...4

These are the decision variables

The objective is to maximize the net income which is the difference between Loan and investment in period 4

Investment income in period 4 = 110% of I4 = 1.1I4

Expense and loan in period 4 = 1.085 L4

So,

Maximize Z =  1.1I4-1.085 L4

Constraints

L1<= 3000

I1<= 4500

L1-I1= 100( Payroll payment)

L2<= 7000

I2<= 8000

L2+1.1I1-1.085L1-I2=120

L3<=4000

I3<= 6000

L3+1.12I2-1.085L2-I3=150

L4<=5000

I4<=7500

L4+1.13*I3-1.085L3-I4=100

1.10I4-1.085L4>=0

Lt, It>=0

Putting this in excel sheet,

See remaining part in pictures attached.

Explanation:

See pictures attached.