The corner points for the bounded feasible region determined by the system of inequalities shown below are O = (0,0), A = (0,6), B = (6,3), and C= (7,0). x+2y s 12 3x + y s 21 х, у 20 If P = ax + by and a, b> 0, determine conditions on a and b that will ensure that the maximum value of P occurs at both B and C.

Q: Find the maximum and minimum values of the function f(x,y,z) = x + 2y subject to the constraints y^2…

A:

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

A:

Q: Find the maximum value of Z = 2x + 3y subiect to the constraints : x +y < 30, y 2 3, 0sy s 12, x -y…

A:

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…

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

A:

Q: Find the minimum value of f(x, y, z) = 2x2 + y2 + 3z2 subject to the constraint 2x − 3y − 4z = 49.

A: Given: Function=f(x,y,z)= 2x2+y2+3z2 Constraint: 2x-3y-4z=49

Q: Prove that if you minimize the square of the distancefrom the origin to a point (x, y) subject to…

A: GIVEN Prove that if you minimize the square of the distancefrom the origin to a point (x, y) subject…

Q: The function ​f(x,y,z)=3x−3y+2z has an absolute maximum value and absolute minimum value subject to…

A:

Q: Find the maximum value of Z = 2x + 3y subiect to the constraints : x +y < 30, y 2 3, 0sy s 12, x - y…

A:

Q: Find the values of​ x, y, and z that maximize xyz subject to the constraint 192−x−8y−16z=0.…

A: Use the lagrangian's multiplier  xyz+λ192-x-8y-16z Partially differentiate with respect to x, y, z…

Q: Maximize the function ƒ(x, y, z) = x2 + 2y - z2 subject to the constraints 2x - y = 0 and y + z = 0.

A: Given:  The function is  f(x,y,z)=x2+2y-z2And subject to the constraints  2x-y=0 and y+z=0

Q: 4. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the…

A: To find the maximum and minimum values of the function f(x,y,z)=xyz subjected to the constraint…

Q: A company makes two types of electronic devices: laptops and tablets. Its business plan says that it…

A: Solution: x is the number of laptops made per day, &amp; y is the number of tablets made Maximum no.…

Q: Find the values of x, y, z that minimize 3x² + 2y² + z² + 4x + y + 3z, subject to the constraint 4 -…

A: Let fx,y,z=3x2+2y2+z2+4x+y+3z   and    gx,y,z=4−x−y−z≡0Apply Lagrange Multiplier method to find…

Q: Find the maximum and minimum values of the function f(x, y, z) subject to the constraints z+y-z-2…

A:

Q: , Find the minimum value of the function f(T, Y, z) = x² +y +z subject to the constraints a +…

A: To find the minimum value of the below function subject to constraints x + 4y + 6z = 2 and x + 7y +…

Q: The production function for a firm is p(x, y) = 68x"y"", where x and y are the number of units of…

A: By Method of Lagrange's multiplier . To maximize fx,y,z subject to gx,y,z=k  Solve system of…

Q: A triangle has variable sides x, y, z subject to the constraint such that the perimeters is fixed to…

A: answer is in next step

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

A: Part b:

Q: (a) Find the critical points of f(r,y) = r² + y² + ry? and determine whether these points are local…

A: (a) Given function is fx,y=x2+y2+xy2. First we will find the critical points of the given function.…

Q: a. [ ] Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = x² + y²…

A: f(x,y)=x2+y2 subject to the constraint  x2-2x+y2-4y=0 Let g(x, y)=x2-2x+y2-4y

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

A:

Q: Find maximum and minumum values of f(x, y, z) = 7x - 14y + 35z subject to the constraint x² + y? +…

A:

Q: Find the maximum and minimum values of the function f(x, y, z)= 3x - y - 3z subject to the…

A:

Q: Draw the region in the xy plane where x+2y = 6 and x 2 0 and y 2 0. Which point in this "feasible…

A:

Q: Find the minimum and maximum of the function z 7z - 4y subject to 7z-3y 2 18 7z+y s 57 What are the…

A: Given z=7x-4y subject to y≥1y≤87x-3y≥187x+y≤57 We will solve it by graphical method The shaded…

Q: roduction function for a firm is p(x, y) = 96xy", where x and y are the number of units of labor and…

A: According  to guidelines  we solve one question. Thanku

Q: Find the extreme values of the function subject to the given constraint. f(x, y, z) = (x - 1)2 +…

A: As per company guidelines we are allowed to solve one equation at a time so i am solving first one…

Q: Also, we must have *0. yz0. Therefore, the above problem can be formulated as follows: find x and y…

A: Given the LPP problem is, Max z=2x+125y12x+13y≤130...112x+23y≤170...2 Converting the given…

Q: Find the minimum value of f(x,y,z) = x 2 + y 2 + z2 subject to two constraints, x + 2y + z = 3 and x…

A: fx,y,z=x2+y2+z2 Lets solve using substitution method- x-y=4⇒x=4+y…

Q: Find the minimum value of h(x, y) = (x − 2)2 + 2xy − (y + 4)2 constraint y=x. subject to the

A:

Q: The corner points for the bounded feasible region determined by the system of inequalities shown…

A:

Q: Find maximum and minumum values of f(x, y, z) = 2x – 4y + 10z subject to the constraint x? + y? + z2…

A: Z27272

Q: Find the maximum value of Z = 2x + 3y +y< 30, y 2 3, 0<ys 12, x – y 2 0, and 0<x < 20. subiect to…

A:

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x - y - 3z subject to the…

A:

Q: The corner points for the bounded feasible region determined by the system of inequalities shown…

A: E is true.

Q: Use Lagrange multipliers to find a relative minimum function value of f if f(x,y,z)= x² + y²+ z²…

A: Here, the given function is: f(x,y,z)=x2+y2+z2 with the two constraints…

Q: The maximum value M and the minimum value m of f(x,y)=x³-2y² subject to the constraint x3+y3=125 are…

A: Apply the Lagrange's multiplier method, ∂f∂x=λ∂g∂x⇒3x2=λ(3x2)⇒3x2(λ-1)=0⇒x=0 ; λ=1Also,…

Q: A satellite television reception station is to be located at point P so that the sum of the squares…

A:

Q: Find the minimum and maxinum of f(x, y, 2) HỰ +2 subject to two constraints, z + 2y +z=8 and z- y =…

A:

Q: 7- 4- 3- -1 2 3 4 5 6 7 8 9 10 Maximize x-5 y for the bounded feasible region displayed above.

A: We have to find the maximum value of (x - 5y) fir the given feasible region in the graph. Using…

Q: A function, z = ax + by, is to be optimised subject to the constraint, r + y = 1 where a and b are…

A: Given that the function to be optimised is z=ax+by subject to the constraint x2+y2=1 where a and b…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = x + y + 5z, subject…

A: The given function f(x, y, z)=x+y+5zg(x, y, z) = x2+y2+z2-4 ∂f∂x=1∂f∂y=1∂f∂z=5

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x – y – 3z subject to the…

A: Given function isfx, y, z=3x-y-3zConstraints arex2+2z2=4andx+y-z=2

Q: Use the method of Lagrange multipliers to maximize the function subject to the given constraint.…

A:

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A:

Q: Minimize f(x,y,z) = 3x2+4y2+6z2 subject to the constraint 3x+7y+8z=20. a.) When the minimum…

A: Given that , fx,y,z=3x2+4y2+6z2 and gx,y,z=3x+7y+8z-20 According to our guidelines , We can answer…

Q: minimize f(z,y,x) =2x2+5y2+6z2 subject to the constraint 4x+5y+8z=28. when the minimum occurs, what…

A: Given, f(x,y,z) = 2x2 + 5y2 + 6z2 subject to constraints 4x + 5y +8z = 28. We have to find the…