Consider the problem minimize f(x, y) = 2y – x² subject to x + y² < 1, x 2 0, y 2 0.

Given the following constraints, find the maximum and minimum values for z.   Constraints:  2x−y≤12 4x+2y≥0 x+2y≤6 Optimization Equation: z=2x+5y Maximum Value of z:  Minimum Value of z:

How can I graph these linear enequalities on a solution set number line? 1) 8x-11 is less than equal to 3x-16 2) 4(x+1)+2 is greater than equal to 3x+6 3) 2x-11 is lee than -3(x+2) 4) 1-(x+3) is greater than equal to 4-2x 5) 1- x/2 is greater than 4 6) 3x is less than 3(x-2) 7) 8(x+1) is less than equal to 7(x+5) +x

min     x1 +  x2 s.t.   3x1 + 2x2 ≥ 36        3x1 + 4x2 ≥ 48         x1, x2 ≥ 0 For the LP problem above, which are the binding constraints?            3x1 + 2x2 ≥ 36     3x1 + 4x2 ≥ 48     x1 ≥ 0     x2 ≥ 0