Formulate the following example as a linear program.

Problem 4. Broker Sonya Wong is currently trying to maximize her profit in the bond market. Four bonds are available for purchase and sale at the bid and ask prices shown in the first table below. Sonya can buy up to 1000 units of each bond at the ask price or sell up to 1000 units of each bond at the bid price. During each of the next three years, the person who sells a bond will pay the owner of the bond the cash payments shown in the second table below. Sonya's goal is to maximize her revenue from selling bonds less her payment for buying bonds, subject to the constraint that after each year's payments are received, her current cash position (due only to cash payments from bonds and not purchases or sales of bonds) is nonnegative. Note that her current cash position can depend on past coupons and that cash accumulated at the end of each year earns 11.111% annual interest. Determine how to maximize net profit from buying and selling bonds, subject to the constraints previously described. Why do you think we limit the number of units of each bond that can be bought or sold?

Table 1: Bid and Ask Prices

Bond

1

2

3

4

Bid Price

980

970

960

940

Ask Price

990

985

972

954

Table 2: Cash Payments

Bond

1

2

3

4

Year 1

100

80

70

60

Year 2

110

90

80

50

Year 3

1100

1120

1090

1110