Find Positive nombers X$ Y Such that X+y = 78 and 24xy a is maximized

Q: Is the point a = [0, 1]T a local minimizer? %3D

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Q: Find a point a* that satisfies FONC (Vƒ(x*) = 0) for f. Then determine if this point is a local…

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Q: find the max im um anel minimum Limits of the functibu n Fix.y) = x"+y"-2x²- 4xy- 2y²

A: The given function is F(x,y)=x4+y4-2x2-4xy-2y2    …..(1) Differentiating partially with respect to x…

Q: D={(1,y) | + 등아 < 6}. 25

A: Use lagarange multipliers

Q: Find the maximum of y = xa − xb on [0, 1], where 0 &lt; a &lt; b. In particular, find the maximum of…

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Q: Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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Q: ! Find the max/min point for z = f(x, y) =-5x² -10y² + 20x+ 20y.

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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: Find two nonnegative numbers x and y such that xy 56 and 7x + 2y is minimized. y =

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Q: 2. Of all numbers whose sum is 30, find the two that have the maximum product. That is, maximize Q =…

A: To Determine: of all numbers whose sum is 50 ,find the two that have the maximum product .That is…

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

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Q: Find two nonnegative numbers x and y such that xy=72 and 9x+2y is minimized.

A: Let the two non negative numbers be x and y Given xy=72 Therefore, y=72x Sum of two positive numbers…

Q: Given ScZand IS -a, what is the maximum value of x+y:x.YESAX+Y1?

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Q: Find the absolute maximum and minimum of the function f(x,y) = 7y + 64x – 3 over the closed region…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.…

A: Given, the function max f(x, y) = 2x + 2xy + y, and the constraint 2x + y = 100. We have to find the…

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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Q: Find the absolute maximum of f(x,y) = 5x2y2 5y2 + 6x2 bounded by y = x, y = 0 and x = 2. Answer:

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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: Let f(x, y) = x² - y² + 2y. Find the absolute maximum and minimum values of f on the region 4x2 + y²…

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Q: Find the area of a parallelogram bounded by the y-axis, the line  x = 2,  the line  f(x) = 8 + 2x,…

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Q: Find two positive numbers x and y that minimize the product xy, and satisfyx + 4y = 120.

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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: All units in a 30-unit apartment building are rented outwhen the monthly rent is set at r =…

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Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: 1. Of all numbers whose sum is 70, find the two that have the maximum product. That is, maximize Q =…

A: Let such two numbers whose sum is 70 and have the maximum product are x and y. So, we have x+y=70…

Q: Find the minimum and maximum values of: f (x, y) = x² + xy bounded by the graphs y = x´ and y =9

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Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Find the local minimum value of f(z, y) = 4 + x² + y7 – 7xy.

A: Explanation of the answer is as follows

Q: Find the local minimum value of f(x, y) = 4 + x15 + y!5 – 15xy.

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Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

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Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: Find the number in the interval [ – 1, – 0.25] so that the sum of that number and its square is…

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Q: Find the absolute maximum of f(x,y) = 3x2y2 + 2y2 + 2x2 bounded by y = x, y = 0 and x = 5.

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Q: Use the method of Lagrange multiplier to find the absolute maximum and absolute minimum values of…

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Q: Find the relative minimum f(x,y)=288y2+x2-x2y

A: According to the given information it is requires to find the relative minimum of the function:

Q: q Find a positive numbers x and y such that x²+y= 48 and their product P(xjy) = xy is maximized. %3D

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Q: Find the number in the interval (-1, -0.25) so that the sum of that number and its square is…

A: Let the function be fx=x+x2 and interval −1,−0.25. In order to function have maximized,…

Q: Find the maximum value of f on the region shown, subject to the constraint g (x, y) = c . At what…

A: a. The maximum value of f is 4. The point at which the maximum occurs is (0, 4).

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = x2 + y? subject to ry =…

A: Given function is fx,y=x2+y2 and constraint is xy=1

Q: Find the local minimum value of f(x, y) = 4 + x1 + yll – 11xy. 11 11

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Q: Eind Positive Numbers XE y Such that X+Y -54$ 1oxy is maximized

A: detailed solution with explanation is given below

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: Use langrage multiplier to maximize f(x,y)=25- x2 -y2 subject to 2x+y=10

A: We have f(x,y) = 25 -x2 -y2 subject to 2x + y =10

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

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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: Find the absolute maximum and minimum values of f(x, y) = x^2 +xy + y^2 - 3x + 3y on the triangular…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positiv Maximize…

A: The given function is;  f(x,y)=sqrt(43-x2-y2) Constraint: x+y-6=0

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.