# Linear Programming

14-5 Two dice are rolled independently and the two numbers that turn up are recorded.

Determine the following:

(a) The probability that the two numbers are odd with values less than 5.

(b) The probability that the sum of the two numbers is 10.

(c) The probability that the two numbers differ by at least 3.

14-15 The number of units, x, needed of an item is discrete from 1 to 6. The probability, p(x), is

directly proportional to the number of units needed. The constant of proportionality is K.

(a) Determine the pdf and CDF of x, and graph the resulting functions.

(b) Find the probability that x is an even value.

18-3 In each of the following situations, identify the customer and the server:

*(a) Planes arriving at an airport.

*(b) Taxi stand serving waiting passengers.

(c) Tools checked out from a crib in a machining shop.

(d) Letters processed in a post office.

(e) Registration for classes in a university.

(f) Legal court cases.

(g) Checkout operation in a supermarket.

*(h) Parking lot operation.

18-10The time between arrivals at the State Revenue Office is exponential with mean value

.04 hour. The office opens at 8:00 a.m.

*(a) Write the exponential distribution that describes the interarrival time.

*(b) Find the probability that no customers will arrive at the office by 8:15 a.m.

(c) It is now 8:35 a.m. The last customer entered the office at 8:26. What is the probability that the next customer will arrive before 8:38 a.m.? That the next customer

will not arrive by 8:40 a.m.?

(d) What is the average number of arriving customers between 8:10 and 8:45 a.m.?

18-22 An art collector travels to art auctions once a month on the average. Each trip

is guaranteed to produce one purchase. The time between trips is exponentially

distributed. Determine the following:

(a) The probability that no purchase is made in a 2-month period.

(b) The probability that no more than 6 purchases are made per year.

(c) The probability that the time between successive trips will exceed 2 month.

18-30 (Use Excel Statistics Tables to give value for calculations)

Consider Example 18.4-2. In each of the following cases, first write the answer

algebraically, and then use excelPoissonQ.xls or TORA to provide numerical answers.

*(a) The probability that the stock is depleted after 3 days.

(b) The average number of dozen roses left at the end of the second day.

*(c) The probability that at least one dozen is purchased by the end of the fourth day, given that the last dozen was bought at the end of the third day.

(d) The probability that the time remaining until the next purchase is at most half a day, given that the last purchase occurred a day earlier.

(e) The probability that no purchases will occur during the first day.

(f) The probability that no order will be placed by the end of the week.

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