An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.30 worth of electricity, and $0.10 worth of steel; the electric industry needs $0.01 worth of coal, $0.04 worthof electricity, and $0.04 worth of steel; and the steel industry needs $0.30 worth of coal and $0.01 worth of steel. The sales demand is estimated to be $3 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand forelectricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand?Set up the input-output matrix.CoalElectricSteelCoal Electric SteelThe coal industry should produce $ billion the electric industry should produce s billion, and the steel industry should produce $(Round the final answer to the nearest billion as needed. Round the elements of the inverse matrix to two decimal places as needed.)billion.

Write the given data in the form of the table.Input/OutputCoalElectricitySteelFinal…

Answered: An economy consists of coal, electric,…

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 patient takes vitamin pills. Each day he must have at least 420 IU of vitamin A, 8 mg of vitamin B,, and 45 mg of vitamin C. He can choose between pill 1, which contains 240 IU of vitamin A, 2 mg of vitamin By, and 5 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 2 mg of vitamin B, , and 30 mg of vitamin C. Pill 1 costs 20¢, and pill 2 costs 60¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy ……of pill 1 and…..? of pill 2. The minimum cost is $….? b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving He is receiving ……IU of vitamin A, …….." mg of vitamin B,, and….. mg of vitamin C more than he needs.
A company manufactures paring knives and pocket knives. Each paring knife requires 3 labor-hours, 7 units of steel, and 4 units of wood. Each pocket knife requires 6 labor-hours, 5 units of steel, and 3 units of wood. The profit on each paring knife is $3, and the profit on each pocket knife is $5. Each day the company has available 102 labor-hours, 157 units of steel, and 123 units of wood. Suppose that the number of labor-hours that are available each day is increased by h. For what values of h will a change of h labor-hours not change the shadow price of labor? The shadow price of labor will not change for shs. (Simplify your answers.)
Gerber Mixed Cereal for Baby contains, in each serving, 60 calories, no Vitamin C, and 11 grams of carbohydrates. Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories, 45% of the RDA of Vitamin C for infants, and 21 grams of carbohydrates. Gerber Apple Banana Juice contains, in each serving, 60 calories, 120% of the RDA of Vitamin C for infants, and 15 grams of carbohydrates.t Assume that the cereal costs 11¢ per serving, the dessert costs 50c per serving, and the juice costs 30c per serving. If you want to provide your child with at least 240 calories, at least 120% of the RDA of Vitamin C, and at least 48 grams of carbohydrates, how can you do so at the least cost? | serving(s) | serving(s) Gerber Mixed Cereal for Baby Gerber Mango Tropical Fruit Dessert Gerber Apple Banana Juice serving(s)
A patient takes vitamin pills. Each day he must have at least 540 IU of vitamin A, 24 mg of vitamin B,, and 70 mg of vitamin C. He can choose between pill 1, which contains 240 IU of vitamin A, 4 mg of vitamin B,, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 4 mg of vitamin B,, and 20 mg of vitamin C. Pill 1 costs 10¢, and pill 2 costs 30¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy of pill 1 and of pill 2. The minimum cost is $ (Simplify your answers. Type integers or decimals.)
Please provide typed answer. Thank you.
2. At the local zoo, Henry the Hungry Monkey requires a very specific blend of Cavendish bananas and plantains as part of his diet. Henry eats 80 pounds total of bananas and plantains per week. The bananas cost $3.12 per pound and the plantains cost $4.52 per pound. If the zoo receives a weekly bill of $312.60 for bananas and plantains, then how much of each does Henry consume per week?
A patient takes vitamin pills. Each day he must have at least 900 IU of vitamin A, 14 mg of vitamin B₁, and 80 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 2 mg of vitamin B₁, and 10 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 2 mg of vitamin B₁, and 15 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 75¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 8 of pill 1 and 0 of pill 2. The minimum cost is $ 2. (Simplify your answers. Type integers or decimals.) b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. mg of vitamin C more than he needs. and He is receiving IU of vitamin A, mg of vitamin B₁, a (Simplify your answers.)
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…
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A forest consists of two types of trees; young (between 0 and 3 m tall) and adults (more than 3 m). Each year, 20% of young trees die, 10% sell for $20 each, 30% remain between 0 and 3 m, and 40% grow taller than 3 m. Each year, 40% of adult trees sell for $50, 20% sell for $20, 30% remain in the forest, and 10% die. What percentage of the trees planted sell for $50?
Need only a handwritten solution only (not a typed one).
An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.20 worth of electricity, and $0.20 worth of steel; the electric industry needs $0.02 worth of coal, $0.04 worth of electricity, and $0.03 worth of steel; and the steel industry needs $0.30 worth of coal and $0.02 worth of steel. The sales demand is estimated to be $1 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand? Set up the input-output matrix. Coal Electric Steel Coal 0.01 0.02 0.30 Electric Steel 0.20 0.04 0.20 0.03 0 0.02 The coal industry should produce $ ☐ billion the electric industry should produce $ ☐ billion, and the steel industry should produce $ (Round the final answer to the nearest billion as…

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