Of all numbers whose sum is 52, find the two that have the maximum product. That is, maximize Q = xy where x + y = 52.

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A: Let each side of the square cut-off from each corner be x in. then the length of the base of the box…

Q: Use lagrange multipliers to find three positive numbers whose sum is 51 and the sum of whose squares…

A: Given that, the sum of the positive number is 51. That is, Fx,y,z=x2+y2+z2 and gx,y,z=x+y+z=51.…

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Q: Of all numbers whose sum is 54, find the two that have the maximum product. That is, maximize Q = xy…

A: The answer is found in step-2

Q: Of all numbers whose sum is 50, find the two that have the maximum product. That is, maximize Q =…

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Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x2 + y? subject to the…

A: Given f(x,y)=x2+y2 and subject to constraint is xy=2 and we need to find the minimum value of given…

Q: Use Lagrange multipliers to find three positive numbers whose sum is 18 and the sum of whose squares…

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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…

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Q: Of all numbers whose sum is 46, find the two that have the maximum product. That is, maximize Q = xy…

A: Given ,           x+y=46           Maximize , Q=xy

Q: The profit equation for for Scotty’s Socks is given by P (q) = (2/3)q3 −(q^2) − 4q + 8, where q is…

A: Given the equation of profitP(q)=23q3−q2−4q+8

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Q: Find two nonnegative numbers x and y with 2x + y = 3 for which the term xy² is maximized. by

A: Given 2x+y=30, we need to maximize xy2

Q: Find two nonnegative numbers x and y for which 2x + y = 30, such that xy2 is maximized.

A: Given that, 2x + y= 30 y = 30 - 2x ................... (1) The function is: f(x, y) = xy2  f(x) = x…

Q: find the values of  x greater than or equal to 0 y greater than or equal to 0 that maximize…

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Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

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 two positive numbers x and y that maximize Q = x2y if x + y = 2.

A: Given function - Q = x2y               ...........(1)And,x+y = 2y = 2-x…

Q: Find two positive numbers with product 256 and whose sum is a minimum

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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: Use the duality method to solve each linear programmin 1. Minimize Z = 29x,+ 10x2 subject to: 3x,+…

A: Given that  Minimum z=29x1+10x2subject to 3x1+2x2≥2                   5x1+x2≥3…

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Q: To graph the maximum domain of the function f(x, y) = Vy – 2 - In [(y – 1)² + x – 1] The green…

A: Solve the given problem.

Q: Of all numbers whose sum is 46, find the two that have the maximum product. That is, maximize Q = xy…

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Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

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Q: the maximum product. That is, maximize Q=xy where x +y 40 re xD and y3=

A: Here, to maximize Q=xy where x+y=40⇒y=40-x So, Q(x)=x(40-x)=40x-x2

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Q: Of all points (x,y,z) that satisfy x+y+4z=24, find one that maximizes (x-1)2 +(y-1)2+(z-1)2

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Q: Find the minimum values for the set of equations; indicate if the solution has on converged. x² +…

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

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Q: Use Lagrange multipliers to find three positive numbers whose sum is 230 and whose product is…

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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: Find the maximizer of f(x, y) = x² + y² subject to 2x + y ≤2, z ≥ 0 and y ≥ 0.

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Q: Maximize B = xy“, where x and y are positive numbers such that x + y = 3. The maximum value of B is

A: To maximize, B=xy2  --(1)Given that x+y2=3   ⇒y2=3-x   substituting in (1)

Q: Of all numbers whose sum is 54​, find the two that have the maximum product. That​ is, maximize…

A: we have to find the value of x and y when Q has maximum value. the solution is following.

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A: Let x be the length of the wire cut for the circle then the length of the wire cut for the square.If…

Q: What necessary conditions are replaced by "minimize"? obeyed by a solution to (1) if "maximize" were

A: To write the  necessary condition for min ∫t0t1F(t,x(t),x'(t))dt with x(t0)=x0

Q: Find a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: Ay 10어 6- (3, 5) 4- (어4) (7, 3) 2- (4, 1) 0어 4 6. 8. 10 N.

A: Here's in the graph there are four constraints, we will check all points which one is maximum.

Q: Suppose x and y are positive integers such that the sum of x^2 and y is 10x. Find the values of x…

A: Given x^2+y=10x.From there find y.

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 positive numbers with product 256 and whose sum is a minimum.

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