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403L Final Exam Review Sheet

  1. According to USA Today, 24% of adults are afraid to fly. If you are planning a family reunion with 150 guests coming from afar (i.e. needing to fly), what is the probability that at least 30 of them will suffer from fear of flying. Approximate your answer to this question using a normal approximation for the binomial random variable.
  2. Write the objective function and all the constraints that comprise the linear programming problem corresponding to the following question. DO NOT SOLVE

    A frisbee manufacturing company makes three styles of frisbees: junior, regular and competition. The company produces frisbees by the case. Producing one case of junior models costs $300 and requires 5.5 hours of labor. Making one case of the regular model costs $350 and requires 7 hours of labor. The competition model costs $420 and requires 7.5 hours of labor per case. The company can spend $40,000 and has available 800 labor hours. The junior frisbees generate a profit of $325 per case, while the regular frisbees generate a profit of $345 per case and the competition frisbees generate a profit of $350 per case. How many of cases each type of frisbee should the company make in order to maximize its profits?

  3. a) Set up the initial simplex tableau for the following linear programming problem.

    Maximize: tex2html_wrap_inline43

    Subject to:

    tex2html_wrap_inline45

    tex2html_wrap_inline47

    tex2html_wrap_inline49 .

    b) Perform one iteration of the simplex method.

    c) Are you now at the optimal solution?

  4. Consider the following linear programming problem and answer (a) and (b) below to find a solution graphically.

    Minimize: tex2html_wrap_inline51

    Subject to:

    tex2html_wrap_inline53

    tex2html_wrap_inline55

    tex2html_wrap_inline57

    tex2html_wrap_inline59 , tex2html_wrap_inline61 .

    (a) On the graph below, shade the feasible region and label it with the letters ``FR''.

    figure9

    (b) Determine the coordinates of the corner points of the feasible region and find the optimal solution(s).

  5. Consider the following linear programming problem.

    Maximize: tex2html_wrap_inline63

    Subject to:

    tex2html_wrap_inline65

    tex2html_wrap_inline67

    tex2html_wrap_inline69

    tex2html_wrap_inline59 , tex2html_wrap_inline61 .

    (a) On the graph below, shade the feasible region and label it with the letters ``FR''.

    figure13

    (b) Let tex2html_wrap_inline75 , tex2html_wrap_inline77 and tex2html_wrap_inline79 be slack variables for the first, second and third constraints listed above. The simplex tableau

    equation17

    corresponds to a basic feasible solution. Which one? (i.e. Determine values of all the variables.) What are the the basic and non-basic variables of this basic feasible solution? Circle the point on the graph which corresponds to this solution.

    (c) Perform one iteration of the simplex method to arrive at a new basic feasible solution. What is the new basic feasible solution? Is this new solution optimal? Circle the point on the graph which corresponds to this solution.

  6. In the process of solving a linear programming problem, a friend obtained the following simplex tableau:

    equation27

    How can you tell that your friend made a mistake somewhere?


    [Note about problem 1: For purposes of the question you need to assume that each guest has a 24% chance of being afraid to fly, independent of all the other guests. I don't think this independence is realistic. If your brother is afraid to fly, that's bound to increase the chance of your being afraid to fly.]



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Lorenzo Sadun
Thu Dec 3 08:21:16 CST 1998