A team tests three cooler designs. A: ice lasts 7 h, cost $4. B: 8 h, $9. C: 5 h, $3. The criterion is ice lasting at least 6 hours. The constraint is a cost of $5 or less. Which design meets both?

Water filter tests: A removes 90% of dirt and flows 20 mL/min through a narrow tube. B removes 60% and flows 50 mL/min through a wide tube. The team wants clean water quickly. Which pair of features should the next prototype combine?

A team drops three parachute prototypes of equal mass. A is dropped from 3 m, B from 5 m, and C from 2 m. B stays in the air longest. Why can the team not conclude that B is the best design?

A team tests one shelf bracket prototype three times and records 3.0 s, 4.5 s, and 4.2 s for how long it held a load. What mean should the team record from these trials?

Bridge tests: A holds 12 N and costs $5. B holds 15 N and costs $8. C holds 9 N and costs $4. The team's constraint is a cost of $6 or less. Design B meets that constraint.

Phone case tests: A survives a 1 m drop, costs $6, mass 80 g. B survives 1 m, $3, 120 g. C survives 0.5 m, $2, 90 g. Every case must survive a 1 m drop, and the team's top priority is low cost. Which design wins?

A team's criteria for a lunch box are that it keeps food cool for 4 hours and has a mass under 500 g. Their test recorded only the temperature after 4 hours. What must they do before choosing a design?

A team's cardboard chair holds 20 kg, but the criterion is 40 kg. They add a second cardboard layer to each leg and run the load test again. What step of the design process is this?

Cup insulation tests: A has 2 mm foam, keeps a drink hot 30 min, mass 60 g. B has 6 mm foam, 55 min, 110 g. The team wants a hot drink and a light cup. What does this pattern in the data show?

Boat hull tests: A is narrow with low sides and carries 300 g. B is wide with low sides and carries 500 g. C is narrow with high sides and survives 8 cm waves, while A and B swamp at 4 cm. Which two features should be combined?

Two clothes-drying rack designs are tested. A dries a shirt in 30 min and costs $8. B dries it in 25 min and costs $12. The budget constraint is $10. Choosing A is correct because B breaks a constraint.

A team tests each of three shelf designs one time. A holds 8 kg, B holds 9 kg, and C holds 8.5 kg before bending. Why should the team run more trials before naming a winner?

A class must build a bird feeder that holds 200 g of seed and stays dry in rain, using only materials from the recycling bin. What is "only materials from the recycling bin" in this design problem?

Glue mixtures are tested once each on paper strips. Mixture A holds 5 N, B holds 5 N, and C holds 2 N before the strip tears. What conclusion do these test data support?

A robot arm must lift 2 kg and fit inside a 30 cm box. A lifts 3 kg and is 35 cm long. B lifts 2.5 kg and is 28 cm. C lifts 1 kg and is 20 cm. Which design fails only because of the size constraint?

A team wants a taller paper tower. Their next test plan changes the amount of tape, the base width, and the paper type all at the same time. What is wrong with that plan?

Helmet pad tests: Design X scores 9 of 10 for comfort and has a mass of 900 g. Design Y scores 7 of 10 and has a mass of 700 g. The constraint is a mass under 800 g. Y is the better choice because X breaks that constraint.

A team times how long each of three fan designs keeps a paper strip lifted. During Design C's trial, someone opened a window nearby. What is the best thing to do with C's result?

A backpack must have a mass under 600 g, hold 5 kg of books, and cost under $20. Design D has a mass of 550 g, holds 4 kg before the seam tears, and costs $15. Which requirement do the test data show D failing?

Lamp tests: Prototype A has a wide shade that spreads light over 2 m but a narrow base that tips at a small nudge. B has a 1 m spread and a wide base that stays upright. What should the next prototype combine?