Lingo 做线性规划 - Financial Applications

Reference: <An Introduction to Management Science Quantitative Approaches to Decision Making, Revised 13th Edition>

Financial Application 1: Management of Welte imposed the following investment guidelines.
1. Neither industry (oil or steel) should receive more than $50,000.
2. Government bonds should be at least 25% of the steel industry investments.
3. The investment in Pacific Oil, the high-return but high-risk investment, cannot be more than 60% of the total oil industry investment.
What portfolio recommendations—investments and amounts—should be made for the available $100,000?

A1: Build mode as below:

A = dollars invested in Atlantic Oil
P = dollars invested in Pacific Oil
M = dollars invested in Midwest Steel
H = dollars invested in Huber Steel
G = dollars invested in government bonds

Finanacial Application 2: Hewlitt Corporation established an early retirement program as part of its corporate restructuring. At the close of the voluntary sign-up period, 68 employees had elected early retirement. As a result of these early retirements, the company incurs the following obligations over the next eight years:

The cash requirements (in thousands of dollars) are due at the beginning of each year.
The corporate treasurer must determine how much money must be set aside today to meet the eight yearly financial obligations as they come due. The financing plan for the retirement program includes investments in government bonds as well as savings. The investments in government bonds are limited to three choices:

The government bonds have a par value of $1000, which means that even with different prices each bond pays $1000 at maturity. The rates shown are based on the par value. For purposes of planning, the treasurer assumed that any funds not invested in bonds will be placed in savings and earn interest at an annual rate of 4%.

A2: Build Model as below

F = total dollars required to meet the retirement plan’s eight-year obligation
B1 = units of bond 1 purchased at the beginning of year 1
B2 = units of bond 2 purchased at the beginning of year 1
B3 = units of bond 3 purchased at the beginning of year 1
Si = amount placed in savings at the beginning of year i for i = 1, . . . , 8