math linear programming

A. Calculations – Must show work for full credit

1. The university is planning the annual orientation program for first-year students to be held the first week of August. All prospective first-year students and their parents have been invited to campus for a 3-day visit. Since summer school will not start until the third week of august, the university will make the dormitories available for most participants in the program.

In order to provide enough free time for the participants to roam around the campus and downtown areas on their own, the dormitories will serve only breakfast. For lunch and dinner, the participants will be encouraged to explore a number of interesting restaurants on and around campus. The dietitians at the dining halls are planning breakfast for the first day of the orientation period. Once the first day’s breakfast menu is determined, the second and third days’ breakfasts will be decided. The dietitians want to provide the participants with a menu that is not only appetizing, but that will also satisfy nutrient requirements at the lowest possible cost.

The dietitians have no problem deciding upon which beverages they will serve: orange juice, tomato juice, coffee, tea, and milk. However, based on their experience in recent years, there has been some disagreement concerning the types of food to serve. After a lengthy discussion, a very simple breakfast is decided upon: scrambled eggs and “ smokies” sausage.

 The dietitian’s responsibility is to provide an adequate amount of the following nutrients: vitamin A, vitamin B, and iron. Another important consideration is that the menu must have the lowest possible cost. The nutritional contents, expressed in milligrams (mg) per scoop of scrambled eggs and per smokie, the minimum nutrient requirements, and the unit costs of foods being considered are:

Food Nutrient Content ( mg)  

NutrientScrambled EggSmokieNutrient Requirement (mg)

Vitamin A3330

Vitamin B4234

Iron1212

Unit Cost8 Cents10 Cents

1.  Determine the objective and design the programming   

2. How do you tell that your result works?

2. Solve the following linear inequality graphically.

4x + 2y is less than, or equal to 15

2x + y is less than or equal to 10

X + y is less than, or equal to 12

X is greater than, or equal to 0

Y is greater than, or equal to 0.

3. Given the following set, create a Dual system

4x1 + 3x2 is greater than, or equal to 30

2x1 + x2 is greater than, or equal to 18

8x1 + 32 x2 = C

4. Given the following set of equations, create a simplex tableau

Maximize P = 60X1 + 100X2

S . t.  X1 + 3x2  is less than, or equal  to  40

         2x1 + 3x2 is less than, or equal to 110