10 May Exercise 5. One die is rolled. Find the probability of rolling a two given that an even number has been rolled. Exercise 6. In a small, rural town in Pennsylvania, 62% of the work force is classified as “blue collar”. It is also known that 72% of the blue collar workers are dog owners and that 56% of the white collar workers are also dog owners. a) Find the probability of randomly selecting a white collar worker form the work force of this town. b) Find the probability of selecting a white collar worker given that the person selected is a dog owner. Exercise 7. Forty honor society inductees must be arranged in rows of eight. How many different arrangements of the honor students are possible? Exercise 8. A professor writes fifteen different essay questions for an upcoming exam. a) If the exam is to be made up of only six of the essay questions, how many different ways can the questions be arranged? b) If each student is instructed to choose four questions to answer, how many different four-question exams can be made? Exercise 9: Testing a Claim: The biogene research company claims that it has developed a technique for ensuring that a baby will be a girl. In a test of that technique, 12 couples all have baby girls. Find the probability of getting 12 baby girls b chance, assuming that boy s and girls are equally likely and that all the gender of any child is independent of the others. Does that result appear to support the company’s claim?
Mary Smith makes pottery by hand in her basement. She has 20 hours available each week to make bowls and vases. A bowl requires 3 hours of labor, and a vase requires 2 hours of labor. It requires 2 pounds of special clay to make a bowl and 5 pounds to produce a vase; she is able to acquire 35 pounds of clay per week. Mary sells her bowls for $50 each and her vases for $40 each. She wants to know how many of each item to make each week to maximize her revenue.
a. Formulate an integer programming model for this problem.
b. Solve this model using the computer.
c. Compare the solution in part (b) with the solution without integer restrictions and indicate if the rounded –down solution would have been optimal.
d. Illustrate (c) graphically.
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