University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2015
Views:

495

Pages:

6
Author:

oele44f2

Section 1: Solve by graphing. Problem 1a: 8x - 10y = 30 3x + 2y = 12 Solution: (4, 0) Problem 1b: 8x - 10y = 30 4x - 5y = 30 Solution: No solution Section 2: Solve by substitution or elimination. Problem 2a: 2(2x - 3y = 9) 3(-2x - 6y = 0) Solution: (-3, -5) Problem 2b: 2(3x - 5y = -13) -6y + 11y = 26 Solution: (4, 2) Problem 2c: 2(3x - 5y = -13) -6y + 11y = 26 Solution: Many solutions Section 3: Solve the system of inequalities by graphing. Problem 3a: x - y ≥ -4 x - 2y ≤ 6 -y ≥ -x - 4 Solution: Shaded region on the graph Section 4: Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function. Inequalities: -5 ≤ y ≤ -3 x + y ≤ 5 -2x + y ≤ 5 Function: f(x, y) = 4x - 3y Vertices: (-4, -3), (-5, -5), (8, -3) Maximum value: 55 at (8, -3) Minimum value: -7 at (-4, -3) Section 5: Word problem about a sporting goods manufacturer making soccer balls and volleyballs. Constraints: 0 ≤ x ≤ 600 0 ≤ y ≤ 400 x + y ≤ 900 x ≥ 200 Profit function: P = 1.2x + y Maximum profit: 1080 at (200, 400) Optimal production: 200 soccer balls and 400 volleyballs Section 6: Word problem about a manufacturing facility filling a rush order for boxes. Variables: x = machine time, y = student time Constraints: 30x + 25y ≥ 290 x ≤ 8 y ≥ 0 Cost function: C = 5x + 10y Optimal solution: (3, 8) Minimum cost: $125 Section 7: Give sets of inequalities that define each of the shaded regions below. Region a: y ≤ 2 y ≥ 0 x ≥ 1 x ≤ 4 Region b: y ≥ 0 x ≥ 0 y ≤ -4/3x + 4 Section 8: Suppose each shaded region in #7 represents the feasible set for a linear programming problem. List the points that you would test in a profit equation. Region a: (1, 0) (1, 2) (4, 0) (4, 2) Region b: (0, 0) (3, 0) (0, 4) Problem 9: Table: | Process | Machine Time | Skilled Labor | Unskilled Labor | |---|---|---|---| | A | 1 | 2 | 3 | | B | 2 | 2 | 1 | Part A: Profit function: P = 50x + 70y Part B: Constraints: x + 2y ≤ 3000 2x + 2y ≤ 3600 2x + y ≤ 3600 x ≥ 0 y ≥ 0 Part C: Graph of the constraints with labeled vertices: (0, 1500), (1200, 0), (600, 1200), (900, 900) Part D: Maximum profit: 10800 at (900, 900) Optimal production: 900 cabinets from Process A and 900 cabinets from Process B