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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 zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2700 mg of iron, 2400 mg of vitamin B-1, and 1800 mg of vitamin B-2, One Maxivite pill contains 500 mg of iron, 200 mg of vitamin B-1, and 100 mg of vitamin B-2, and costs $0.05. One Healthovite pill provides 100 mg of iron, 150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.06. Complete parts (a)-(c) below. (a) What combination of Maxivite and Healthovite pills will meet the walrus's requirement at lowest cost? What is the lowest cost? Set up the linear programming problem. Let m represent the number of Maxivite pils, h represent the number of Healthovite pills, and c represent the total cost in dollars. Minimize c= 0.05m + 0.06h subject to 500m + 100h 2 2700 200m + 150h 2 2400 100m + 150h 2 1800 m20, h 2 0. (Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.) The best combination of pilts that moets the walrus's…
A famine relief effort is being mounted and there are three types of food bundles that can be flown out during each delivery. Bundle 1 has 4 kg. of flour, 4 kg. of sugar and 12 litres of water. Bundle 2 has 12 kg. of flour, 4 kg. of sugar and 4 litres of water and Bundle 3 has 8 kg. of flour, 8 kg. of sugar and 8 litres of water. The relief agency has 5200 kg. of flour, 3792 kg. of sugar and 6000 litres of water for each shipment. Bundle 1 can provide for 10 people between deliveries, Bundle 2 for 8 people and Bundle 3 for 11 people. How many bundles of each type should the relief agency send on each flight in order to maximize the number of people being fed. Do this problem by setting up a linear programming problem and determining the vertices of the feasibility set. Enter the number of bundles of types 1, 2, and 3 (in that order) into the answer box below, separated with commas.
The Cheery Cherry Chair Company makes three types of chairs, the Montegue, the Capulet, and the Verona. Each chair requires assembly, finishing, and a certain amount of wood to make. The assembly area can be used for at most 10 hours per day. To keep him busy, the finishing person needs to work at least 6 hours per day. Producing a Montegue requires 1 hour of assembly, 2 hour of finishing, and 9 board feet of wood. Producing a Capulet requires 1 hour of assembly, 1 hour of finishing, and 9 board feet of wood. Finally, producing a Verona requires 2 hour of assembly, 1 hour of finishing, and 3 board feet of wood. If the company wants to minimize the amount of cherry wood used, how many should they make of each model? (It is possible to complete a fractional part a chair in a given day; in the long run you end up with completed chairs.) Number of Montegues = Number of Capulets = Number of Veronas = How many board feet of cherry wood would be used each day?

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