# Problem 12 You have the following two matrices. Find A + B.

Problem 12: You have the following two matrices. Find A + B.A = (2,1  B = (3 4  the  parentheses are actually one large one around all four #’s       1 5)         2 1)Problem 13: Using matrices A and B from problem 12, find the matrix (2A – 3B).Problem 14: Using matrices A and B from problem 12, find the matrix (A X B).Problem 15: You have the following two matrices. Find C X D.C = (1 2 4  D = (3 4 1  the parentheses are actually one large one around          1 5 2           1 2 1  all four #’s         0 3 3)         4 0 2)Problem 16: You have worked a system down to the following augmented matrix. Which one of the following is true of the solution?    (1 0 1 |5      the parentheses are actually one large one around all four #’s      0 1 3 |13      0 0 0 |0)a.) There are no solutions to this system.b.) There are infinite solutions to this system.c.) There is only one solution to this system.d.) The solution cannot be determined from the given information.Problem 17: You have worked a system down to the following augmented matrix. Which one of the following is true of the solution?    (1 0 2 | 9                the parentheses are actually one large one around all 13 #’s     0 2 3 | 14     0 0 0 | 8)a.) There are no solutions to this system.b.) There are infinite solutions to this system.c.) There is only one solution to this system.d.) The solutions cannot be determined from the given information.Problem 18: Find the inverse of the following matrix.A = (1 2              the parentheses are actually one large one around all four #’s       4 3 )Problem 19: Given a (n x n) matrix Y and a (n x n) matrix Z, if (Y x Z) equals the identity matrix, then which one of the following statements are true.a.) Matrix Y and matrix Z are equivalent.b.) Matrix Y and matrix Z have no solutions.c.) Matrix Z is the inverse of matrix Y.d.) Matrix Z cannot be multiplied by matrix Y.Problem 20: Given the input-output matrix and the output of the following industry, determine the amount consumed internally by the production process.A = ( 2.10 1.20  X = ( 40        1.35 2.15 )         20)Problem 21: Graph the solution of the inequality 2x + 3y ≥ 6.Problem 22: Graph the solution of the inequality 3x + 2y ≤ 6.Problem 23: Graph the solution of the equality 4x – 2y = 0.Problem 24: Graph the solution of the inequality Y ≤ -2.Problem 25: Graph the feasible region of the following system.2x + y ≤ 10-x + 3y ≤ 6Where x ≥ 0, and y ≥0.Problem 26: Maximize z = 15x + 9y, subject to5x + 3y ≤ 305x + y ≤ 20x ≥ 0, y ≥ 0Problem 27: What is the maximum value of the objective function given the information below?Corner points (x, y)         Max Z = 6x + 5y(0, 0)(0, 10)(3, 8)(6, 5)(8, 0)Problem 28: (worth 3 points) P&R makes two grades of gears for industrial machinery, standard and heavy duty. The process requires two steps. Step 1 takes 8 minutes for the standard gear and 10 minutes for the heavy duty gear. Step 2 takes 3 minutes for the standard gear and 10 minutes for the heavy duty gear. The company’s labor contract requires that it use at least 200 labor-hours per week on step 1 equipment and 140 labor-hours on step 2 equipment. The materials cost \$15 for each standard gear and \$22 for each heavy duty gear. How many of each gear should be made to minimize cost?

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