7) There is an island on which all the people are of one of two types: either vegetarians or cannibals. Initially,two vegetarians and two cannibals are on the left bank of a river. With them is a boat that can hold amaximum of two people (two vegetarians, two cannibals, or one of each). You need to find a way totransport all the vegetarians and cannibals to the right bank of the river. At no time can the number ofcannibals on either bank outnumber the number of vegetarians! Otherwise, disaster befalls the vegetarians.Create a graph to solve this problem.Question: How many possible solutions are there? Consider each solution to be a description of how thefour people get across the river. If you create a graph to solve this, you should be able to look at the possiblemoves and determine how many ways there are to move everybody across.O 5O 2O 3O 1O Something else

Answered: Image /qna-images/answer/750cc80d-6709-43f0-99d0-2d81af6ac36c.jpg

Answered: 7) There is an island on which all the…

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 diet is to contain at least 8 units of vitamins, 9 units of minerals, and 10 calories. Three foods, Food A, Food B, and Food C are to be purchased. Each unit of Food A provides 1 unit of vitamins, 1 unit of minerals, and 2 calories. Each unit of Food B provides 2 units of vitamins, 1 unit of minerals, and 1 calorie. Each unit of Food C provides 2 units of vitamins, 1 unit of minerals, and 2 calories. If Food A costs P30 per unit, Food B costs P20 per unit and Food C costs P30 per unit, how many units of each food should be purchased to keep costs at a minimum? 3.
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, and 2 units of fat, and will contain 40 calories. Each ounce of nuts will supply 2 units of protein, 1 unit of carbohydrate, and 4 units of fat, and will contain 50 calories. Every package must provide at least 2 units of protein, at least 13 units of carbohydrates, and no more than 16 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories? Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized? Z=
Now, let's discuss the difference cases of solution to a given system of linear equations. There are three different cases: a) The system has exactly one solution (one set of solution). b) The system has no solution c) The system has infinitely many solutions. In this assignment, you will need to give an example a system of two linear equations (2 equations, 2 unknowns) for the three cases.
An individual needs a daily supplement of at least 405 units of vitamin C and 210 of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 30 units of vitamin C and 14 units of vitamin E, while each ounce of food II contains 15 units of vitamin C and also 28 units of vitamin E. The total supplement of these two foods must be at most 33 ounces. Unfortunately, food I contains 24 units of cholesterol per ounce and food II contains 28 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol. amount of food I oz amount of food II oz minimum cholesterol units
A cat breeder has the following amounts of cat food: 120 units of tuna, 110 units of liver, and 70 units of chicken. To raise a Siamese cat, the breeder must use 3 units of tuna, 2 of liver, and 2 of chicken, while raising a Persian cat requires 2, 1 and 3 units respectively per day. If a Siamese cat sells for $13, and a Persian cat sells for $14, how many of each should be raised in order to obtain maximum gross income? Set up the initial simplex tableau. ** Set up the initial simplex tableau for the problem. Let x, be the number of Siamese cats, and let x₂ be the number of Persian cats. Begin by filling in missing terms for constraints. 3x₁ + 2x₂ 5 is the constraint on tuna consumption. 2x₁ + x₂ is the constraint on liver consumption. 2x, +3x₂ s chicken consumption. is the constraint on
Mark's company makes two games (Zeldor and Pekomon) using two machines (A and B). Each unit of Zeldor that is produced requires 25 minutes processing time on machine A and 35 minutes processing time on machine B. Each unit of Pekomon that is produced requires 32 minutes processing time on machine A and 29 minutes processing time on machine B. Available processing time on machine A is forecast to be 1,600 minutes and on machine B is forecast to be 3,045 minutes. If Zeldor can be sold at a price of 2,500 pesos per unit and Pekomon is 2,700 pesos per unit, a. What are the vertices of the constraints? (check all that apply) (32,25) (58, 25) (58, 35) (0, 105) (0, 50) (0,0) (50,0) (25,38) (58, 32) (35, 32) b. How much of each game should the company produce to maximize profit c. How much is the maximum profit?
U.S. Trucking pays its drivers $40,000 per year, while American Trucking pays its drivers $38,000 per year. For both firms, truck drivers average 240,000 miles per year. Truck driving jobs are the same regardless of which firm one works for, except that U.S. Trucking gives each of its trucks a safety inspection ever 50,000 miles, while American Trucking gives each of its trucks a safety inspection every 36,000 miles. This difference in safety inspection rates results in a different rate of fatal accidents between the two companies. In particular, one driver for U.S Trucking dies in an accident every 12 million miles while one driver for American Trucking dies in an accident every 15 million miles. What is the value of a trucker’s life implied by the compensating differential between the two firms?
A diet is to contain at least 1596 units of carbohydrates, 2700 units of proteins, and 2568 calories. Two foods are available: F₁ which costs $0.02 per unit and F2, which costs $0.04 per unit. A unit of food F₁ contains 2 units of carbohydrates, 5 units of proteins and 6 calories. A unit of food F₂ contains 8 units of carbohydrates, 5 units of proteins and 4 calories. Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutrition requirements. Corner points of the feasible region: If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)). Minimum cost is: $ when F₁ = and F2 = units units.
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, and 2 units of fat, and will contain 40 calories. Each ounce of nuts will supply 3 units of protein, 1 unit of carbohydrate, and 4 units of fat, and will contain 50 calories. Every package must provide at least 3 units of protein, at least 7 units of carbohydrates, and no more than 12 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories? Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized?

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