4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2
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- Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥84Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 2x + 9y subject to the following. 2x + 5y ≤ 50 x + 5y ≤ 45 x + y ≤ 14 (x,y)= f=Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 20x + 12y + 12z subject to the following. x + z ≤ 45 x + y ≤ 30 y + z ≤ 45 (x,y,z)= f=
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