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Minimize the function x^2+y^2+z^2 subject to constraint x+2y+3z=6 and x+3y+9z=9
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- Find the maximum value of the function f=4x+2yf=4x+2y subject to the constraintsx+3y≤8x+3y≤82x+4y≤62x+4y≤6Assume that both variables are non-negative.The maximum value is f=f=. This occurs when x=x= and y=y=.A company needs 250,000 items per year. It costs the company $1,200 to prepare a production run of these items and $12 to produce each item. If it also costs the company $1.50 per year for each item stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized.Solve min x1-x2-2x3 problem by means of Lagrange multipliers under the constraints of x1+x2+x3=5 and x12+ x22 =4. Explain what the values of Lagrange multipliers mean?
- Find the minimum value of f(x,y,z) = x 2 + y 2 + z2 subject to two constraints, x + 2y + z = 3 and x - y = 4.Find the minimum value of z=3x+9y subject to the constraints x+3y≤10 ; 3x+y≥10; y≤x ; x≥0; y≥0 using graphical methodExpress the problem as a system of equations using slack variables. (Use s1, s2, ... for the slack variables.) Maximize subject tofirst equationsecond equationthird equationobjective equationz =420x1 + 270x2 + 10x3, 6x1 + 7x2 + 12x3≤50 4x1 + 18x2 + 9x3≤85 x1−2x2 + 14x3≤66 x1≥0, x2≥0, x3≥0.
- Find the minimum value of f (x, y) = xy subject to the constraint 5x - y = 4 in two ways: using Lagrange multipliers and setting y = 5x -4 in f(x,y).A company needs 450,000 items per year. It costs the company $2,160 to prepare a production run of these items and $14 to produce each item. If it also costs the company $1.50 per year for each item stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized. items/runThe minimum value of f(x,y) = x^2y + 3y^2 - y subject to the constraint x^2 + y^2 = 10 is.........?