Find two positive numbers x and y such thatx + 2y 50 and (x + 1)(y+ 2) is a maximum.

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: Given f(x,y) = 22+2y2-3xyconstraint            x+y = 4                                    y = 4-x…

Q: Find the maximum value of z = xy2 subject to 2x2 + y2 = 294; x ≥ 0, y ≥ 0. z =

A: Given information : z = xy2  subject to  2x2 + y2 = 294;  x≥0;  y≥0.

Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A: fx,y=3x2+4y2 and x+4y=104⇒x=104-4yTo find:Extremum and determine its type.

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? +y² + z²…

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Q: Find the quadratic function f(x) = ax + bx +c that goes through (2,0) and has a local minimum at (0,…

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

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Q: Find the maximum value of xy if it is required that 2x +7y = 35

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Q: Find two positive numbers x and y such that x+y=60 and xy^3 is maximum.

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Q: Find the maximum value of xy if it is required that 2x + 7y = 35 %3D

A: Given  2x+7y = 35  y=(35-2x)/7 Let M = xy  To maximize the value of xy=M we need to differentiate…

Q: 5. y2 2x y26-x fx, y) = 4x+ 3y Minimum: Maximum: | | | | |

A: We need to find maximum and minimum values of f(x,y).

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Show that the function f(x,y) = x³ + y³ – 63(x +y) + 12xy is maximum at (–7,–7) and minimum at…

A: Given function: fx,y=x3+y3-63x+y+12xy Formula Used: D-Test: For each point a,b where fxa,b=0 ,…

Q: Suppose that x and y are two positive numbers, and suppose that r+ 2y = 30. Find the maximum value…

A: Given that: x+2y=30…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

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Q: f(x, y) = 2x2 + 3y2 - 4x - 1, x2 + y2 s 16 maximum minimum

A:

Q: Find 3 numbers x, y, and z such that their sum is 32 and P=xy^2z is a maximum.

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Q: Find the maximum of f (x, y, z) = z subject to the two constraints x2 + y2 = 1 and x + y + z = l.

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Q: Suppose that f(x, y) 3x + 3y* 2xy Then the minimum value of f is

A: We have to solve given problem:

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

Q: Find positive numbers x and y such that x + y = 48 and 5x2y + 10 is maximized.

A: Given that, x + y= 48 y = 48 - x ................... (1) The function is: f(x, y) = 5x2 y+ 10 f(x) =…

Q: Find the maximum value of f(x,y) = 25 - x - y on the line x+ 4y = 17. %3D

A: First-order derivative test for Maximum value : - The slope of a function is determined by its first…

Q: The function f(x, y) = 2x² + 4y² + 2x³ has a local maximum at the point (0, 0). Select one: O True O…

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Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: Maximize f(x,y)=64-(x-2)2-(y-2)2 subject to the contraint x2+y2=8 when the maximum occurs, what is…

A: Given, the function is f(x, y) = 64 – (x – 2)2  - (y – 2)2 subject to constraints x2 + y2 = 8.

Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: 1. Find the maximum value of f(x, y) = 4xy where x > 0 and y > 0, subject to the constraint 9. = 1.

A:

Q: Determine the maximum and minimum values of f(x,y,z) = 3x + 6y + 2z, subject to 2x^2 + 4y^2 + z^2 =…

A: Using the lagrange multipliers

Q: Find the maximum value of ƒ(x, y) = 49 - x2 - y2 on the line x + 3y = 10.

A:

Q: . Find the minimum value of C = 3x + 5y subject to %3D 4x +3y > 240 4x + y > 120 y > 0

A: 4x+3y≥240 divide both sides by 240 4x240+3y240≥240240 x60+y80≥1 compare this equation with the…

Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

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Q: Find three positive numbers x, y, and z whose sum is 21 and product is a maximum.

A: There are two different questions in the image. According to our guidelines, we can solve only one…

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x + 3y = 10.

A: Solution of given question is written in below steps.

Q: The function f(x, y) = -2x² + 4y² - 12 has a local maximum at the point (0,0). Select one: O True…

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Q: f(x) = 2x3+az? 12z has alocal maximum at z -2,then a

A: f(x)=2x3+ax2-12x  has a local maximum at x=-2then we have to find the value of a

Q: The population density of a city is given by P(x,y) = - 20x-20y +200x + 600y + 170, where x and y…

A:

Q: Of all numbers whose difference is 4, fınd the two that have the minimum product. x= y=

A: Given that  Difference of two number is 4 and we need to find the two numbers whose product is…

Q: Suppose that x and y are two positive numbers, and suppose that x + 2y = 30. Find the maximum value…

A: Given data:   The first equation is x+2y=30. The expression for the function is f(x,y)=(x+1)(y+3).…

Q: Find the maximum value of z = xy2 subject to 8x2 + y2 = 1944; x > 0, y 2 0. z =

A: Given z=xy2 and condition 8x2+y2=1944; x≥0, y≥0 Let F=xy2+λ8x2+y2-1944 Partially differentiating…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: We have to find maximum and minimum values using Lagrange multipliers

Q: Find the absolute maximum of f(x,y) = 9x²y² + 4y2 + 4x² bounded by y = x, y = 0 anC Answer:

A:

Q: Find the absolute maximum and the absolute minimum of the function f(x,y, z) x² + y² + z², subject…

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Q: Find the absolute maximum of f(x,y) = 5x²y² + 4y² + 6x² bounded by y = x, y = 0 and x = 4. %3D…

A: The given function is: f(x,y)=5x2y2+4y2+6x2Bounded Region is:  y=x,  y=0,  x=4

Q: Find the absolute maximum value and absolute minimum value of f(x, y) = 2a2 + 2y² + 4y – 1 on the…

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Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

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Q: Minimize f(x,y)=x2-y2 subject to the contraint 3x-7y=-4 when the minimum occurs, what is  a. x?…

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Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A: Solution:-  the given constraints are  f(x,y) = xy and 14x+y=8 we have to find extremum....

Q: If x² + y² < z < 1, find the maximum and minimum of the function u(x, y, z) = x + y + z

A: We have to find the maximum and minimum of the function.

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.