li'm, n are positive integers and the equations x² + mx + 2n = 0 and x² + nx + m = 0 have real rots. Find the minimum value of m + n. (

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: need help with 2and 3 not number 1 !!!

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Q: Find two positive integers such that their sum is 10 and maximize and minimize the sum of their…

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Q: two cities A and B are 8 km and 12 km, respectively, north of a river which runs due east. City B…

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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…

A: Product of two positive number is 750. The sum of one and 10 times of another is minimum.

Q: Two cities A and B are 8 km and 12 km, respectively, north of a river which runs due east. City B…

A: Given,  Two cities A and B are 8 km and 12 km respectively , north of a river which runs due…

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A: According to given,    Let x be length of the portion that is bent into a circle   Therefore, 4-x=…

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: Find the minimum value of f (x, y) = xy subject to the constraint 5x - y = 4 in two ways: using…

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Q: person in a boat is 24 km from a shore and wishes to reach a point 20 km down shore (from a point…

A: person in a boat is 24 km from a shore and wishes to reach a point 20 km down shore (from a point…

Q: a. Solve max f(x,y,z) = 3x² + y problem by means of Lagrange multipliers under the constraints of…

A: The Lagrange's multiplier method can be used to calculate the maximum or the minimum value of the…

Q: of 4x + 6y subject to x + y 2 1, x – y > 2. O -7 None of the others There is no minimum 9. O 3

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Q: Find two positive numbers whose sum is 15 so that the sum of their square is minimum,

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Q: A piece of 1m wire is cut into two parts, one bent into the shape of a circle and the other into the…

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Q: a. Solve max f(x, y,z) = 3x² + y problem by means of Lagrange multipliers under the constraints of…

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Q: A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a…

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Q: A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: Let x be the distance down the shore where the boat is landed. t1= time to row to the shore = 52+x23…

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: A wire of length 10 is to be cut into two pieces, one being bent to form a square and the other to…

A: It is given that a wire of length 10 units to be cut into two pieces. Let one piece of wire be x…

Q: 6. Find the extreme valucs of f(r,y) = ry subject to the constraint 4x2 + y? = 8 by using the method…

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Q: b. Solve min x, -x, - 2x, problem by means of Lagrange multipliers under the constraints of x, +x,…

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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: From a tract of land, a developer plans to fence a rectangular region and then divide it into two…

A: Given: Cost of fence on outside = $20 per foot Cost of middle fence = $8 per foot Area of each lot =…

Q: Find two positive number whose sum is 15 so that the sum of their square is minimum.

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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…

Q: A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: Let 'x' be the distance from point to the landing position. Given situation in graph is represent as

Q: 19. A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of…

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Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

Q: A wire of length L is cut into pieces, one being bent to form a square and the other form an…

A: Assuming that the wire is cut in 2 pieces of length x and L-x where the first is used to make a…

Q: Find two positive numbers whose product is 50 such that the sum of the first plus 2 times the second…

A: Given, Product of 2 positive number is 50  First number+2(second number)=S, is a minimum.

Q: Solve min x1-x2-2x3 problem by means of Lagrange multipliers under the constraints of x1+x2+x3=5 and…

A: To determine maxima and minima of the function with respect to some constraints then follow as Find…

Q: What is the particular solution for y′=−6x+3 that passes through the point (−4,−8)? Do not include…

A: The given differential equations is y′=−6x+3.

Q: A farmer wishers to fence off three identical adjoining rectangular pens, each with 300 square feet…

A: Given, Cost of the fence of outer boundary of the pens = $3 per foot Cost of the fence of two…

Q: Con company has total costs cl) = 21000-1Sxt O.YxZ and total renenves iven by eco ミ345¢-0.^xて、find…

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Q: Determine two positive numbers whose product is 4 such that the sum of their squares is minimum.

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Q: Use the Lagrange multiplier method to solve Minimize z = x} + x + x Subject to x, + 2x, + 3x3 = 7…

A: We have to solve the following problem using the Lagrange multiplier, Min z=x12+x22+x32 Subject to :…

Q: )A wire of length L is cut into pieces, one being bent to form a square and the other o form an…

A: Given problem is :

Q: How would you divide a 27 inch line into two parts of length A and B so that A+B=27 and the product…

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Q: simplex method

A: We have to solve the given problem by simplex method.

Q: Minimize Z=8x+12y subject to 4x+6y214, 4x+5y9, x>0, y20 M=?

A: Given LPP is Minimize  Z = 8x + 12y Subject to  4x + 6y ≥ 14, 4x + 5y ≥ 9, x ≥ 0, y ≥ 0

Q: Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm…

A: Let the three sides or edges of the rectangular box be a,b and c in cm. Surface area of the box will…

Q: a. Solve max f(x, y, z) = 3x² + y problem by means of Lagrange multipliers under the constraints of…

A: Since you have asked multiple question, we will solve first question for you. If you want other…

Q: Suppose the product of x and y is 49 and both x and y are positive. What is the minimum possible sum…

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Q: A river flows between the lines x = 3 and x = 4. Where should a bridgebe constructed to minimize the…

A: A river flows between the line x=3 and x=4. Bridge constructed to the path from O(0,0) to P(5,4).

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: Create a 2nd order, homogeneous, linear IVP, that is not guaranteed to have a unique solution at…

A: Let's a take a 2nd order, homogeneous, linear IVP. For second order differential has a unique…

Q: A piece of wire of length 69 is cut into two pieces. One piece is bent into a square and the other…

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