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Mathematics Worksheet
🏭 Operations Research
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After this worksheet you can
Check feasibility against constraints.Write objective functions.Write resource constraints.Understand where linear-programming optima occur.📚 Quick Recap
Operations research applies mathematical modeling and optimization to real-world decision-making — helping organizations run more efficiently by finding the best way to allocate limited resources.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Constraint 4x + 5y ≤ 100: is (15, 5) feasible?
2Constraint 4x + 5y ≤ 100: is (20, 10) feasible?
3$20/unit of A and $35/unit of B: the objective is:
4In linear programming, the optimum occurs at:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5A point satisfying all constraints is .
64(15) + 5(5) = .
7Constraint: 4x + 5y ≤ 100. Is (15, 5) feasible?
8Constraint: 4x + 5y ≤ 100. Is (20, 10) feasible?
9$20 per unit of A and $35 per unit of B: write the objective function.
🚀 Section C · Challenge ● CHALLENGE 5
10Labour ≤ 80 h; A takes 4 h, B takes 8 h. Write the constraint.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-B | 5 feasible 6 85 7 = Yes, 85 ≤ 100 8 = No, 130 > 100 9 = Maximize P = 20a + 35b | 10 = 4a + 8b ≤ 80