7.73 Trade offs, Optimization, and Constraints Worksheet

Prototype test data for a small wind-turbine blade show several trade-offs. The team should first screen for cost, mass, and minimum output, then choose the highest scoring valid option. Limits: cost ≤ $16, mass ≤ 290 g, score ≥ 7. Test evidence: - Prototype 1: cost $14, mass 265 g, output score 8.2 - Prototype 2: cost $20, mass 280 g, output score 9 - Prototype 3: cost $11, mass 250 g, output score 6.2 - Prototype 4: cost $15, mass 275 g, output score 7.4 Which design is optimized?

Design trade-off review: For the storm-drain leaf screen, low cost and low mass matter, but the final choice must also meet the minimum drainage score. Limits: cost $15 or less and mass 255 g or less.,,Science Test evidence:,,Science - Prototype 1: cost $19, mass 245 g,Science - Prototype 2: cost $10, mass 215 g,Science - Prototype 3: cost $14, mass 240 g,Science - Prototype 4: cost $13, mass 230 g,Science "Which choice gives the strongest allowed design rather than just the highest raw score?,A. Prototype 1 — it breaks the cost constraint because $19 is above $15. | B. Prototype 2 — it does not reach the minimum drainage score of 6.5. | C. Prototype 4 — it meets all constraints and has the highest valid drainage score. | D. Prototype 3 — it is valid

The design team is screening for the strongest leak prevention score for a storage bin gasket, but only among designs that satisfy every constraint. Constraints: cost ≤ $14; mass ≤ 220 g; leak prevention score ≥ 7.5. Test evidence: - Prototype 1: cost $9, mass 180 g, leak prevention score 6.7 - Prototype 2: cost $13, mass 205 g, leak prevention score 7.9 - Prototype 3: cost $12, mass 195 g, leak prevention score 8.7 - Prototype 4: cost $18, mass 210 g, leak prevention score 9.5 Which choice gives the strongest allowed design rather than just the highest raw score?