11) A consumer's level of utility from consuming a certain good s is given by thefollowing function:U(x) = 1.5x² - 12Due to a shift in the consumer's taste and preferences they will now derive 2 moreunits of utility for consuming the same amount of good x as before.(a)Sketch the original utility function of good .x.(b) Why is it necessary that x > 0?(c) Determine the new utility function of this company.(d) Using your graph in (i) sketch the transformed utility function.for x > 0

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Answered: 11) A consumer's level of utility from…

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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Suppose demand is given by p = 1600 − x. Find the maximum revenue.
4. At Wally Motors, an auto engineer, in testing a new engine on one of its new models, found that the efficiency e of the engine as a function of the speed s of the car was given by e = 0.768s – 0.00004s. Here e is measured in percent and s is measured in km/hr. What is the maximum efficiency of the engine?
Please let me know how to find out the answer for (b) using the substitution method. I know how to get the functions for (2) as shown. Question: A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost. (a) Formulate this as a linear…
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1. Suppose the function C(r) represents the cost to produce rope as a function of the length of the rope. (a) What can you conclude about C from the statement "The cost of production is increasing at a decreasing rate"? Pick one of positive, negative, zero, or other. If other, please explain. i. C"(r) is ii. C"(r) is (b) What can you conclude about C from the statement "The cost of production is decreasing at an increasing rate"? Pick one of positive, negative, zero, or other. If other, please explain. i. C"(r) is ii. C"(r) is
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1. Describe how the graph of the function can be obtained from one of the basic graphs: 1 y = x y = 22 y = VI y = r3 y = VI y y = |r| (a) f(x) = (x+ 3)² (b) f(r) = x2 +3 (c) f(x) = 12 - %3D (d) h(x) = -VI (e) h(x) = V- 1 (f) g(x) = 1 (g) g(x) = (h) g(x) = |x+2| – 3 (i) f(x) = VI + 2 (6) f(x) =D -글V-1 (k) f(r) = 2VT– 4 (1) f(r) = 2V - 4 4 (m) f(r) = . 2 (n) f(x) = 5 - (0) f(x) %3D 옮교3-4 (p) g(x) = -(x – 3)2 + 5 4.
1. Consider the following function: f (x) = 3x – 2x2 a. Find the derivative function f'(x) using the limit definition of the derivative. b. Use the derivative function to evaluate f'(-1) and f'(2) Given the graph of a function f(x), which is shown to the right, sketch the graph of its derivative f'(x), on the same xy-plane. *Assume the scales of the x-axis and the y-axis are equal.* 2.

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