MATHEMATICAL PROGRAMMING PROBLEMS 12 hrs

Econ 480 MATHEMATICAL PROGRAMMING PROBLEMS

For each of the following problem:

a) Express the problem in mathematical notation.

b) Write it GAMS notation and run the program to solve the problem.

c) Report the results on a separate paper. Specifically, report:

i) The optimum levels of the decision variables.

ii) The value of the objective.

iii) Interpret the marginal values of the constraints, including the meaning of a

zero marginal value.

d) Open your *.LST file, edit out the page breaks, print, and attach after the report

page.

1. San Bernardino Social Services agency is trying to design a minimum-cost meal

that will be used in feeding the area’s poor. The meal is to consist only of seaweed and

tofu but must meet the following nutrient requirements: calories 300 units, protein 250

units, and vitamins 100 units. The nutrient content per ounce of each food is as follows:

Seaweed Tofu Minimum

Nutrition Requirement

Calories 20 15 300

Protein 10 25 250

Vitamins 10 4 100

Seaweed costs $0.02 per ounce and Tofu costs $0.04 per ounce. Determine the amount of

seaweed and tofu that should go into a meal to minimize cost.

2. The production of type A, B, and C transistors requires processing in each of five

locations of a firm’s manufacturing facility. The price per unit on these products are

$1.07, $0.86, and $0.98, respectively and the costs per unit are $1, $0.80, and $0.90,

respectively. The processing times required in each location (in minutes) and the total

minutes available per production period are shown below. Determine the amount of each

type of transistor this company should produce to maximize profits.

Time Required in Location (minutes)

L1 L2 L3 L4 L5

Transistor

A 3 1 2 5 2

B 1 1 4 3 5

C 2 2 1 4 4

Total time

Available in 3,500 2,000 3,000 5,000 3,000

Locations

3. Coyote Publishing prints its Mathematical Economics textbook in plants in

Boston, Atlanta, Denver, Seattle, and San Bernardino. The books are then shipped to

distribution centers in Newark, Chicago, Dallas, and Los Angeles. Table below gives

the information on cost of shipping a book from the production plants to distribution

centers, production capacity at each plant, and quantity demanded at each distribution

center. Find the lowest cost way of supplying the textbook to each distribution center.

Distribution Center

Newark Chicago Dallas Los Angeles Production

Plant Capacity

Boston $0.20 $0.30 $0.40 $0.60 40,000

Atlanta 0.35 0.40 0.45 0.50 10,000

Denver 0.30 0.20 0.30 0.40 15,000

Seattle 0.50 0.40 0.30 0.30 15,000

San- 0.70 0.50 0.45 0.20 20,000

Bernardino

Demand 20,000 40,000 30,000 10,000

4. Marketing department must select a mix of advertising in order to reach a

minimum of 1 million adult males, 2 million adult females, 0.5 million senior citizens,

and 1.5 children. The cost per unit of advertising is: television $200, radio $15,

magazines $90, and newspaper $30. Determine the number of units of each

advertisement that will meet the marketing requirements at a minimum cost.

Number of People Reached per Unit

Television Radio Magazine Newspaper

Target

Adult Males 100 5 50 30

Adult Females 300 20 160 5

Seniors 40 10 5 25

Children 100 40 10 5