You blindfold your friend. You give him a bowl that contains 10 silver marbles and 6 black marbles. What is the minimum mumber of balls your friend needs to pick to be sure that they pick out all 6 black marbles? (The marbles are selected without replacement - once a marble is chosen it is not put back into the bowl).
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- Answer the following questions. 5. What is the term for the arrangement that selects r objects from a set of ii objects when the order of the r objects is not important? What is the formula for calculating the number of possible outcomes for this type of arrangement?The Operations Manager of a construction company wants to assign four contractors to four jobs in such a way as to minimize the time taken to complete four buildings of a special kind and size. Based on experience, the times taken (in months) for each contractor to complete each job are given in the table below. Jobs Contractor 1 2 3 4 1 15 15 16 14 2 20 18 16 19 3 24 26 24 23 4 30 35 38 25 Required:- Using the Hungarian (manual) method, determine the optimal assignment of contractors to jobs in order to minimize the total time taken to complete the jobs. Indicate this overall time and show all working. 2. Write an LP formulation that could be used to solve this problem with the relevant LP software packages.A company is taking bids on four construction jobs. Their bids, in thousands of dollars, are given below. Job 1 Job 2 Job 3 Job 4 Contractor 1 50 46 42 40 Contractor 2 51 48 44 - Contractor 3 - 47 45 45 A dash indicates that the contractor did not bid on the given job. Contractor 1 can do only one job, but contractors 2 and 3 can each do up to 2 jobs. Determine the minimum cost assignment of contractors to jobs.
- A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs P100 to make a daytime call and (because of higher labor costs) P150 to make an evening call. On average, daytime calls reach wives 30% of the time, husbands 10% of the time, and neither of these 60% of the time, whereas evening calls reach wives 30% of the time, husbands 30% of the time, and neither of these 40% of the time. Staffing considerations mean that daytime calls must be less than or equal to half of the total calls made. How many should be interviewed at each period to minimize the cost of completing the survey? fomulate the LP Model; identify the decision variables used in the model; and determine the optimal solution using graphical method.A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operations manager of a large taxi company selects of 40 taxis and finds the average age of the taxis is 8.2 years. The of the population is 2.3 years. At can it be concluded that the average age of the taxis in his company is less than the national average?A direct sale company started out with two members in the first generation. It is the policy of the company that each member has to recruit another two new members under him or her. Assuming that every member fulfils this condition, find the minimum number of generations such that the total number of members exceeds 1200.
- A casino game consists of selecting two balls, without replacement, from an urn containing 4 balls numbered 1 through 4. The amount that you win (in dollars) is the minimum of the numbers on the two balls. How much should be charged to play this game if the casino wants to make $0.30, on average, each time the game is played?A large local dinner is open each weekday from 6am until 8pm. Each waitstaff begins his/her shift 6-hour shift either at 6am, 8am, 10 am, noon or 2pm. To determine how many waitstaff should begin at each of the above 5 times, the owner, based on her knowledge of her customers, has determined the minimum number of waitstaff that is required during each 2- hour time slot to give her customers the service that they expect. This information, along with the wages** that are paid to each waitstaff for the 6-hour shift that they work, appears in the following table. Time slot minimum required wages for 6-hour shift ** 6am – 8am 2 $70 8am – 10am 4 $60 10am – noon 7 $75 noon – 2pm 9…What is the five-number summary for {12.5, 11.2, 10.9, 13.6, 19.9, 9.2, 2.7}? Group of answer choices A). Minimum Value = 12.5Q1 = 11.2Median = 13.6Q3 = 9.2Maximum Value = 2.7 B). Minimum Value = 2.7Q1 = 10.9Median = 13.6Q3 = 9.2Maximum Value = 19.9 C). Minimum Value = 2.7 Q1 = 9.2Median = 11.2Q3 = 13.6Maximum Value = 19.9 D). Minimum Value = 9.2Q1 = 13.6Median = 9.2Q3 = 19.9Maximum Value = 13.6
- Suppose that you randomly selected 22 adults. If 25% of the population smoke,a) Using the Range Rule of Thumb, what is the minimum number of usual smokers we can expect to get out of 22 adults?Note: Round all answers to two decimal places.b) Using the Range Rule of Thumb, what is the maximum number of usual smokers we can expect to get out of 22 adults?Note: Round all answers to two decimal places.c) Would it be unusual to randomly select 22 smokers and get 10 smokers? Explain! Yes, since 10 is not between the maximum and minimum usual values. No, since 10 is between the maximum and minimum usual values. d) If we randomly selected 22 adults and found 10 smokers in the group, what could we conclude? We can conclude that 25% of smokers is probably incorrect, and that the percentage of smokers is greater than 25%. We cannot conclude that the 25% of smokers is probably incorrect.A coding supervisor has two full-time coders who average 35 productive hours per week. A standard of 20 minutes per chart has been established as the departmental coding standard. The facility anticipates an increase in the number of discharges since a new wing to the facility is nearing completion. It is anticipated that the number of discharges will increase to a total of 300 discharges to be coded per week. Will new staff be required and, if so, how many additional coders will be needed?The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…