OM-HW ASSIGNMENT: LINEAR PROGRAMMIN (20 pts.) Note: You are expected to present all your works fully and manually using the blank space for a full credit Otherwise, 1-2 pts, only will be given to each question without a full manual answer. me: 01. Which of the choices below constitutes a simultaneous solution to these equations? (2 pts.) (1) 3X + 2Y = 36 and (2) 5x + 4y = 64 ? a. X 8, Y=6 b. X = 4, Y -0.5 c. X= 1, Y = 2 d. X = 2, Y= 1 e. None of the above 02. What combination of X and Y will yield the optimum for this problem? (3 pts.) Maximize Z = $3X + $15Y subject to: (1)2X + 4Y 12 and (2) 5X + 2Y = 10. a. X = 2.0, Y = 0.0 b. X = 1.0, Y = 5.0 c. X = 0.0, Y = 3.0 d. X = 0.0, Y = 5.0 e. None of the abow _03. What combination of X and Y will provide a minimum for this problem? (3pts.) Minimize 2 - X + 3Y subject to: (1) 2X + 4Y212 and (2) 5X + 2Y 2 10 a. X = 6.0, Y = 0.0 b. X = 5.0, Y = 0.0 CX = 1.0, Y - 25 d. X = 2.5, Y = 1.0 e. None 04. For the constraints given below, which point is in (within the feasible solution space of this maximization problem (1) X1 + X2 s 5, (2) 2X1 + 2x2 26, (3) 3X1 - 2x2 s6 (4 pts.) a. X1=4.0, X2-3.0 b. X1-3.0, X2-5.0 c. X1=1.0, X2=1.0 d. X1-2.0, X2-2.0 e. None _05. What combination of X and Y will yield the optimum for the is L.P. problem (4pts)? Maximize Z = 2x + Y subject to: (1) X+YS 3; (2) X 2Y S 2; and (3) XS 2 at=0.0Y-2.0 b. X-2.0, Y=0.0 CX-2.0, Y-1.0 d. X = 1.0, Y-2.0 .X-4.0, Y = 2.0 06. Consider the graphic L.P. problem below: Max(Z) - $30X - $10 subject to: (1)X + 2Y S6 and (2) $5X + 2Ys 10 What is the possible maximum profit from this linear programming problem? (4 pts.) a $30 a. $55 b. $60 c. $ 70 d. 150 e. None of the above