PROBLEM 6 A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes of removal, the fish population increases by 10% each month. However, factoring in all causes, 80 fish are lost each month. Give a recurrence relation for the population of fish after n months. How many fish are there after 5 months? If your fish model predicts a non-integer number of fish, round down to the next lower integer.
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Q: PROBLEM 6 A lake initially contains 1000 fish. Suppose that in the absence of predators or other…
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1This is a recurrence relations problem In Mayville, 90% of the existing dog licenses are reissued each year, and 1200 new licenses are issued. in 1995 there were 15,000 dog licenses issued. a. Write a difference equation and inital conditions describing the number of dog licenses Mayville will issue n years after 1995. b. How many dog licenses will Mayville issue in 2004? c. If the present trend continues, how many dog licenses can Mayville expect to issue after many years?Problem 13-21 (Algorithmic) A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table: State of Nature Rezoning Approved Rezoning Not Approved Decision Alternative S1 S2 Purchase, d1 610 -190 Do not purchase, d2 0 0 If the probability that the rezoning will be approved is 0.5, what decision is recommended?Recommended decision = What is the expected profit?Expected profit = $ fill in the blank 2 thousands. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during…
- A company that operated 10 hours a daymanufactures two products on threesequential processes. The following tablesummarizes the data for the problem:Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = f…A iPhone store starts by selling 100 iPhone pre-ordered in week zero and expects to sell an average of 15%more each week after that. How many iPhone is the store expected to sell in week 4?
- Consider a service facility with four clerks. Clerk one works at rate 14/hour; Clerk two at rate 18/hour; Clerk three at rate 20/hour; and Clerk four at rate 16/hour. All service times are independent and exponential. If when you arrive there is already one person waiting, what is your expected waiting time?A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…
- Problem 2. Last year, in a sample of 1200 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product A, there are 300 of these people said they never did. This year, if a consumer sends in a rebate claim form, he will get 5 reward points. Observe 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product A this year, 200 of these people said they never did. a/ Does this data strongly suggest that the true proportion of such consumers who never apply for a rebate claim after purchasing the product A last year is greater than this year? Test the hypotheses at significance level 0.05 b/ Calculate an lower confidence bound at the 97% confidence level for the true proportion of such consumers who never apply for a rebate claim after purchasing the product A this yearProblem IIPSuppose that for a recent admissions class, an Ivy League college received 2,851 applications for early admission. Of this group, it admitted 1,033 students early rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.Problem 12P Problem 13P Problem 14P Problem 15P Problem 16P Problem 17Pa. Use the data to estimate P(E), P(R), and P{D).b. Are events fand D mutually exclusive? Find P (E n D).c. For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early…Suppose in a tournament with only three players left, first place receives $6,000, second place receives $3,000, and third place receives $500. You have a 32% chance of winning first place, 30% chance of winning second place, and 38% chance of winning third place. a. What would be your expected winnings in this tournament? b. The tournament organizer gives you the option to continue playing or stop and split the total prize money, proportional to your current standings. If you currently have 700 of the 1800 chips currently in play, how much would you win if you stopped playing and split the winnings? c. Based on parts a and b, should you continue playing or stop and split the money? Why?