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Mathematics Worksheet
🎯 Optimization
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Maximize or minimize with derivatives.Solve budget-constrained problems.Distinguish constrained from unconstrained problems.Interpret optimal values.📚 Quick Recap
Optimization is the mathematics of finding the best possible outcome — the maximum profit, minimum cost, or most efficient use of limited resources.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1P(x) = −3x2 + 120x − 200 is maximized at x =:
2The maximum profit P(20) is:
3A $500 budget with items at $25 each buys at most:
4Optimization with additional limits is called:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Set P′(x) = to find candidates.
6P′(x) = −6x + 120 = 0 gives x = .
7For P(x) = −3x2 + 120x − 200, find the x that maximizes P.
8Using the previous result, find the maximum profit.
9A budget of $500 allows items at $25 each. Find the maximum quantity.
🚀 Section C · Challenge ● CHALLENGE 5
10What is the difference between unconstrained and constrained optimization?
💭 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 0 6 20 7 = x = 20 8 = P(20) = 1000 9 = 20 items | 10 = Constrained must satisfy additional limits; unconstrained has none