A banking system requires Personal Identification Numbers (PINS) that satisfy the following constraints. (1) Must consist of only decimal digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. (2) Must have length at least 5, and at most 8. (3) Must not be the customer's birth date. (Here, a birth date would be encoded as a 6 digit number, so for instance May 3, 1998 would be 050398) How many different valid PINS are there?
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- Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college$60,000, while each section of Computer Methods has 10 students and earns the college $20,000. Assuming the college wishes to offer a total of seven sections, to accommodate 220 students, and to bring in $288,000 in revenues, how many sections of each course should it offer?The Center for Information Technology at State Univer-sity has outgrown its office in Bates (B) Hall and is mov-ing to Allen (A) Hall, which has more space. The move will take place during the three-week break between the end of summer semester and the beginning of fall semes-ter. Movers will be hired from the university’s physical plant to move the furniture, boxes of books, and files thatthe faculty will pack. The center has hired a local retailcomputer firm to move its office computers so they willnot be damaged. Following is a list of activities, theirprecedence relationships, and probabilistic time estimatesfor this project:Determine the earliest and latest start and finish times, thecritical path, and the expected project duration. What is theprobability the center will complete its move before thestart of the fall semester?A hunger-relief organization has earmarked between $2 million and $2.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.25 million (inclusive), and Country B is to receive at least $1 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.80. How should the aid be allocated if the money, in millions, is to be utilized most effectively according to these criteria? Hint: If x and y denote the amount of money, in millions of dollars, to be given to Country A and Country B, respectively, then the objective function to be maximized is P = 0.4x + 0.8y.
- The head of the department of management at Mitil University has noticed that the four secretaries in the department office seem to spend a lot of time answering questions from students that could better be answered by the college advising office, by the faculty advisors, or simply from the available literature; that is, course schedules, catalogs, the students handbook, and so on. As a result the department head is considering remodeling the office with cubicles so student do not have easy access to the secretaries. However, before investing in this project the head has decided to conduct a work sampling study to determine the proportion of time the secretaries spend assisting students. The head arranged for a graduate assistant to make observation for the sample, but the graduate student's schedule enabled her to make only 300 random observations in the time allotted of the time, somewhat less than the head anticipated. a. Given the number of observations that were included in the…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.Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $13,000. Assuming the college wishes to offer a total of six sections, accommodate 210 students, and bring in $253,000in revenues, how many sections of each course should it offer? Finite Math section(s)Applied Calculus section(s) Computer Methods section(s)
- Verify that in the example to the right, the same result isobtained if the constraint x + y = 20 is used to eliminate x rather than y.A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines, and plant Il needs at least 32 engines. The company can send at most 120 engines to these assembly plants. It costs $30 per engine to ship to plant I and $40 per engine to ship to plant Il. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant Il gives similar $10 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? How many engines should be shipped to each plant to minimize shipping costs, subject to the given constraints? The number of engines to send to plant I is() The number of engines to send to plant Il is() What is the minimum shipping cost, subject to the given constraints?$ ()The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 34 units of the Star model and 40 units of the Prostar model per hour, and line 2 can assemble 170 units of the Star model and 40 units of the Prostar model per hour. The company needs to produce at least 306units of the Star model and 200 units of the Prostar model to fill an order. If it costs $200 per hour to run line 1 and $600 per hour to run line 2, how many hours should each line be run to fill the order at the minimum cost?
- The head of the department of management at State University has noticed that the four secretaries in the departmentaloffice seem to spend a lot of time answering questions fromstudents that could better be answered by the college advising office, by faculty advisors, or simply from the availableliterature; that is, course schedules, catalogues, the studenthandbook, and so on. As a result, the department head isconsidering remodeling the office with cubicles so studentsdo not have easy access to the secretaries. However, beforeinvesting in this project the head has decided to conduct awork sampling study to determine the proportion of timethe secretaries spend assisting students. The head arrangedfor a graduate assistant to make observations for the worksample, but the graduate student’s schedule enabled her tomake only 300 random observations in the time allotted forthe study. The results of the work sampling study showedthat the secretaries assisted students 12% of the time, somewhat…The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit? Group of answer choices A)700 homeless patients and 1,100 high-income patients B)1,200 homeless patients and 600 high-income patientsC)700 homeless patients…The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit?
