Mathematics

Imagine using math to explain how you know your friends and acquaintances. Were any of the people in your life introduced to you through another friend or acquaintance?

In this Discussion, you will create a visual representation that models relationships similar to the “six degrees of separation” as presented in your readings.

Chapters 14, paying special attention to the beginning of Section 14.1.

Select a favorite television series, movie, or novel with an extensive cast of characters that you consider interesting. Determine a relationship that exists among some, but not all, of the characters.

Consider the following graph, which represents the one-way airfare between five cities.

 

a. First use a graph tool like Graph Creator to represent the information in the table. Use vertices to represent the cities and weights on appropriate edges to show the airfares.

b. Next, assume that you are a salesman who lives in one of the cities (pick any city except for A) and required to fly to all four of the other cities and return to your home city. Describe how you would use the Nearest Neighbor Method to determine the optimal route. What is the total cost for this Hamilton circuit?

  •  Write a system of linear equations in three or four variables to solve exercises 47-48.

    47. Three foods have the following nutritional content per ounce.
    Calories Protein Vitamin C
    Food a 40 5 30
    Food B 200 2 10
    Food C 400 4 300

    If a meal consisting of the three foods allows exactly 660 calories,25 grams of protein and 425 milligrams of vitamin c, how many ounces of each kind of food should be used?

    48. A furniture company produces three types of desks, a children model, an office model, and a deluxe model.
    Each desk is manufactured in three stages: cutting, construction, and finishing. The time requirements for each model and manufacturing stage are given in the following table.
    Children Model Office Model Deluxe Model
    Cutting 2hr 3hr 2hr
    Construction 2hr 1hr 3hr
    Finishing 1hr 1hr 2hr

    each week the company has available a maximum of 100 hours for cutting,100 hours for construction and 65 hours for finishing. If all available time must be used, how many type of desk should produce each week?

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