Systems of inequalities with absolute value, and linear programming
Grade 11 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Noah shades the graph of y ≥ |x − 2| + 1 together with y < −x + 9. Which point is in the shaded region?
- (4, 5)
- (0, 2)
- (3, 4)
- (6, 6)
Pia shades the graph of y ≤ −|x + 1| + 6 together with y > x − 2. Which point is in the shaded region?
- (−1, 7)
- (0, 3)
- (2, 0)
- (3, 0)
Ren shades the graph of y ≥ |x − 3| − 2 together with y < 4. Which point is in the shaded region?
- (8, 6)
- (3, −4)
- (7, 4)
- (3, 0)
Zee shades the graph of y > |x + 2| together with y ≤ 6 − x. Which point is in the shaded region?
- (−2, 3)
- (−6, 3)
- (4, 7)
- (1, 3)
Flour 2x + y ≤ 14; oven x + y ≤ 10; at least 3 cookie trays, y ≥ 3. Esme bakes x muffin trays and y cookie trays. The figure lists the limits. Which limit does the plan (6, 3) break?
- The plan is allowed: it meets the limits
- y ≥ 3
- 2x + y ≤ 14
- x + y ≤ 10
Time 2x + 3y ≤ 24; paper x + y ≤ 9; at least 4 posters, x ≥ 4. Jun makes x posters and y banners. The figure lists the limits. Which limit does the plan (3, 5) break?
- x ≥ 4
- x + y ≤ 9
- The plan is allowed: it meets the limits
- 2x + 3y ≤ 24
Soil x + 4y ≤ 24; pots x + y ≤ 9; at least 2 large plants, y ≥ 2. Luz sells x small and y large plants. The figure lists the limits. Which limit does the plan (3, 1) break?
- x + 4y ≤ 24
- x + y ≤ 9
- y ≥ 2
- The plan is allowed: it meets the limits
Lines x + y = 10 and 2x + y = 14 meet at a corner of Noah's bracelet-sale region. Profit is P = 3x + 2y dollars. What is P at that corner?
Lines x + 2y = 14 and x + y = 9 meet at a corner of Ren's kite-sale region. Profit is P = 4x + 3y dollars. What is P at that corner?
Lines 2x + y = 16 and x + y = 11 meet at a corner of Zee's poster-sale region. Profit is P = 6x + 2y dollars. What is P at that corner?