Find the minimum value of w = 4x, + 2x, + x3 subject to the constraints 2x, + 3x, + 4x, < 14 3x, + x, + 5x, > 4 x1 + 4x, + 3xz > 6 where x,> 0, x,>0, and x, > 0.

Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day. 0 Graph the system of inequalities, remember to include x >0 and y > 0 in your graph to get full credit. You will need to include four lines. 25 24 VI

Maximize 54 - x - y, subject to the constraint x+ 7y - 50 = 0. The maximum value of 54 - x - y subject to the constraint x+ 7y - 50 = 0 is. (Type an exact answer in simplified form.)

9. In each part, determine whether the given 3-tuple is a solution of the linear system (a) (3, 1, 1) 2x1 - 4x₂ - x3 = X3 X₁ - 3x₂ + 3х1 — 5x2 — 3х3 (b) (3,-1, 1) x3 = = = (c) (13, 5, 2)