Answered: · x”+ 4x' + 5x = 8(t − ñ) + d(t − 2π);…

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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Problem 1 If company A manufactures t-shirts and sells them to retailers for US$9.80 each. It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers. The demand for its product is p = 15 -D5 its production cost per unit is US$5.00 and its fixed cost are the same as for company A . (1) Derive the total revenue function, R(x) for company A. (ii) Derive the total cost function, C(x) for company A. (iii) Derive the profit function, II(x) for company A.
In 1967, the population of Clements, PA was 7,000, and in 1974 the population was 12,000. Should the populatio grow linearly, in what calendar year (to the nearest whole calendar year), would it reach 50,000? If instead the population grew exponentially, how many fewer years would it take to reach 50,000?
Problem 3: Sam is interested in buying a TV but knows they will have to sell it in 5 years. If Sam buys an LG TV, they know it will decrease in price by $15 per year on average. If Sam buys a Samsung TV, they know it will decrease in price by 10% per year on average, Both TV's cost $899.99 to buy now. Which TV will be worth more after 5 years, and by how much? 5
Let's create a mathematical model for the following problem: A chemical company produces a chemical mixture for a customer in 1,000-pound batches. The mixture contains three components: mercury, zinc, and potassium. The mixture must meet specific formula specifications provided by the customer. The company wants to determine the amount of mixture that can meet all requirements and minimize the total cost. The customer provides formula specifications for each batch of the mixture as follows: The mixture must contain at least 200 pounds of mercury. The mixture must contain at least 300 pounds of zinc. The mixture must contain at least 100 pounds of potassium. The cost per pound for mercury is $4, for zinc is $8, and for potassium is $9.
A small plant manufactures riding lawn mowers. The plant has a net fixed cost (leases, insurance, and so on) of$56000/day and variable costs (labor, materials, and so on) of $1600 per unit produced. The mowers are sold for $2000each unit per day. Write down the appropriate cost and revenue equations for the problem respectively. Using theseequations, answer the following questions:(a) How many units must be manufactured and sold each day for the company to maintain break-even trade?(b) Plot both equations simultaneously in a graph, and clearly indicate break-even point, equilibrium point andequilibrium price in this trade to maintain revenue as expected. Interpret the significance of the regions to the left- andright-side of the break-even point in this business.
Question 6 of 16 Ali, the CEO of a manufacturing company, decided to expand the product offering of his business to include the manufacture of a specific model automotive unit. To include this product, his business would incur fixed costs of $365,000 per year and variable costs of $6 per unit. He plans to sell each unit for $88. a. Calculate the number of units he would have to manufacture to break even. Round up to the next whole number b. While manufacturing the unit, he realized that an additional fixed cost of $3,000 per year was required, and also realized that to be more competitive in the market he had to drop the selling price by 20%. What is the new break-even volume? Round up to the next whole number

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· x”+ 4x' + 5x = 8(t − ñ) + d(t − 2π); x(0) = 0, x '(0) = 2