EYDeluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: a type A, x, vessei has 60 deluxe cabins and 160 standard cabins, whereas a type B vessel, y, has 80 deluxecabins and 120 standard cabins. Under a charter agreement with the Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their15-day cruise in May. It costs $58,000 to operate a type A vessel and $54,000 to operate a type B vessel for that period.(a) How many of each type of vessel should be used to keep the operating costs C to a minimum?The minimum is C =(b) Suppose C = cx + 54,000y. Find the range of values that the cost of operating a type A vessel, the coefficient c of x, can assume without changing the optimal solution.≤CM(c) Find the range of values that Requirement 1 for deluxe cabins can assume. (Requirement 1 pertains to the deluxe cabin requirement.)< (Requirement 1) ≤at (x, y) =(d) Find the shadow price for Requirement 1 for deluxe cabins. (Round your answer to the nearest cent.)$Need Help?Read ItWatch It

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A bus system needs to be set up from Village of Westmont to Hinsdale (2.5 miles), then continues to Berwyn (8.5 miles), and finally terminates its run to Cicero (1 mile). The operating time is 55 minutes, the policy headway is 30 minutes, and the minimum terminal time is 19 minutes (including 6 minutes terminal time at each location of Clarendon Hills and Berwyn, and 7 minutes at Cicero). It has been established that the peak-hour demand is 500 passengers per hour and 50-seater buses are available, which can safely accommodate 25 standees. Assume the load factor is 0.8. Design the bus system
You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 18 defrosted beef patties, and 14 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bun, double cheeseburgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of cheese. How many of each should you make? plain burgers double cheeseburgers regular cheeseburgers xxx
For his classes, Professor Wright gives three types of quizzes, objective, recall, and recall-plus. To keep his students on their toes, he has decided to give at least 20 quizzes next quarter. The three types, objective, recall, and recall-plus quizzes, require the students to spend, respectively, 10 minutes, 30 minutes, and 60 minutes for preparation, and Professor Wright would like them to spend at least 12 hours(720 minutes) preparing for these quizzes above and beyond the normal study time. An average score on an objective quiz is 5, on a recall type 6, and on a recall-plus 7, and Dr. Wright would like the students to score at least 130 points on all quizzes. It takes the professor one minute to grade an objective quiz, 2 minutes to grade a recall type quiz, and 3 minutes to grade a recall-plus quiz. How many of each type should he give in order to minimize his grading time?
A theater owner has to fill 1,000 seats in her largest theater. She can fit 2 children or 1 adult per seat. Based on this information, which combinations are on the budget constraint?
Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 11 calls per hour. The arrival rate is 22 calls per hour. How many extension lines should be used if the company wants to handle 90% of the calls immediately?4 lines What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places.L = ?????????? What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal places.40 %
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An automobile company produces cars in Los Angeles and Detroit and has a warehouse in Atlanta.The company supplies cars to customers in Houston and Tampa. The costs of shipping a car betweenvarious points are listed in the table below, where a blank means that a shipment is not allowed. LosAngeles can produce up to 1100 cars, and Detroit can produce up to 2900 cars. Houston must receive2400 cars, and Tampa must receive 1500 cars. (Include your formulations to receive credit. Thinkcarefully about the transhipment locations.) (a) Determine how to minimize the cost of meeting demands in Houston and Tampa. (b) Modify the answer to part (a) if shipments between Los Angeles and Detroit are not allowed. (c) Modify the answer to part (a) if shipments between Houston and Tampa are allowed at a cost of$5 per car.
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 K most 120 engines to these assembly plants. It costs $30 per engine to ship to plant I and $50 per engine to ship to plant II. 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 II is
You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 15 buns, 20 defrosted beef patties, and 14 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bun, double cheeseburgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of cheese. How many of each should you make? plain burgers = ___ double cheeseburgers = ___ regular cheeseburgers = ___

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