3. Ifis subject tof(x, y)=7xyx² + y²14(x + y)= 49find a global maximum stationary point and its value, a global minimum stationary pointand its value as well as another stationary point that is neither a global maximum nor aglobal minimum.

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Answered: 3. If is subject to f(x, y) = 7xy x² +…

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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4) The cost of making x items is C(x)=15+2x. The cost p per item and the number made x are related by the equation p+x=25. Profit is then represented by px-C(x) [revenue minus cost]. a) Find profit as a function of x b) Find x that makes profit as large as possible c) Find p that makes profit maximum.
If a continuos function f has relative minimum, then f should have absolute minimum True/false
1 b) i) Find the stationary point of the function y = x. Note that e In(x). = ii) You are told that this stationary point is a global maximum. Which number is greater, e or ne?
9. In words, explain the difference between an absolute minimum and a global minimum.
Let fx) = x + 2x - 8. For what value(s) of x does fx) have a local minimum?
6. A company produces x units of product A and y units of product B (both in hundreds per month). The monthly profit equation (in thousands of dollars) given by P(x, y) = -4r + 4xy – 3y + 4x + 10y + 81 (A) Find P.(1,3) and interpret the results. (B) How many of cach product should be produced each month to maximize profit? What is the maximum profit?
I understand number 6 but not number 7
Firm's production is represented by z=10x1/2y1/2. z=amount of output. x=amount of labor used. y=amount of capital used. Labor cost= 20 dollars per unit, Capital cost= 80 dollars per unit. Part a) 100 units are currently being made as the output. Labor's cost minimizing quantity=20. Capital's cost minimizing quantity=5. Draw a graph of this with both isocosts and isoquants. Part b) The business wants to make the output increase from 100 units to 140 units. In the short run, capital is fixed. What is the amount of labor needed? Show this in your graph in part a. Calculate the new total cost. Part c) In the graph from part a, draw and label a point that shows capital's and labor's cost minimizing level in the long run if the business wants to make 140 units.

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3. If is subject to f(x, y) = 7xy x² + y² - 14(x + y) = 49 find a global maximum stationary point and its value, a global minimum stationary point and its value as well as another stationary point that is neither a global maximum nor a global minimum.