- Define variables: Let x = number of Cabinet X, y = number of Cabinet Y.
- Objective function: Maximize storage volume V = 8x + 12y (cubic feet).
- Constraints:
- Cost: 10x + 20y ≤ 140 → x + 2y ≤ 14
- Space: 6x + 8y ≤ 72 → 3x + 4y ≤ 36
- Non-negativity: x ≥ 0, y ≥ 0
- Graph the feasible region using the constraints.
- Find corner points: (0,0), (0,7), (4,5), (12,0).
- Evaluate V at each corner point:
- V(0,0) = 0
- V(0,7) = 84
- V(4,5) = 92
- V(12,0) = 96
- Maximum volume is 96 cubic feet at (12,0).
- Buy 12 units of Cabinet X and 0 units of Cabinet Y.
- Define variables: Let h = number of hamburgers, d = number of hot dogs.
- Objective function: Maximize profit P = 0.33h + 0.21d (dollars).
- Constraints:
- Hamburgers: 10 ≤ h ≤ 40
- Hot dogs: 30 ≤ d ≤ 70
- Total items: h + d ≤ 90
- Graph the feasible region using the constraints.
- Find corner points: (10,30), (10,70), (20,70), (40,50), (40,30).
- Evaluate P at each corner point:
- P(10,30) = 9.60
- P(10,70) = 18.00
- P(20,70) = 21.30
- P(40,50) = 23.70
- P(40,30) = 19.50
- Maximum profit is $23.70 at (40,50).
- Sell 40 hamburgers and 50 hot dogs.
Parent Tip: Review the logic above to help your child master the concept of linear programming worksheet and answers.
