Elise Questions — Alex Dutton Education

🐶 Challenge 1: The Puppy Pen Maximer

You have exactly 24 meters of fencing to build a rectangular yard. Slide to change the width, and find the dimension that gives your puppy the largest play area!

🐶

11m

Adjust Width (m): 1m

1 meter 11 meters

Width 1 m

Length 11 m

Perimeter 24 m

Current Area: 11 m²

Your High Score: 11 m²

🎉 Awesome! You found the maximum area of 36 m²! A square ($6\text{m} \times 6\text{m}$) always maximizes area for a fixed perimeter!

👕 Challenge 2: The Concert T-Shirt Hustle

Find the price sweet spot. Base price is $10 (100 buyers). Raise the price by $1, lose 5 sales. Drop it by $1, gain 5 sales. Where is the maximum profit?

Customer Demand 100 Buyers

1 shirt icon = 2 customers

Set T-Shirt Price: $10

$5 (Low price, high sales) $25 (High price, low sales)

T-Shirts Sold 100

Total Revenue $1,000

Current Revenue:

$1,000

Your Max Revenue: $1,000

🎉 Boom! You optimized the revenue to $1,125 by charging exactly $15 per shirt. Raising the price further turns too many customers away!

📦 Challenge 3: Shipping Box Efficiency

Start with a 10 in × 10 in cardboard sheet. Cut equal squares of size x out of each corner and fold up the flaps to make a box. Try fractional cuts to find the perfect volume!

Cardboard Grid (10" x 10")

Corner Cut Size (inches): 1.0"

0.5 inch (shallow) 4.5 inches (deep)

Height 1"

Base Length 8"

Base Width 8"

Current Volume: 64.0 in³

Your High Volume: 64.0 in³

🎉 Awesome Discovery! If using integers, a 2.0" cut wins with 72 in³. But by testing decimals, did you find that a 1.7" cut gets you even higher (~74.1 in³)? You just did calculus without knowing it!

🧁 Challenge 4: Cupcake Delivery (Route Minimizer)

Deliver cupcakes starting from Home to three friends (A, B, and C) and then return Home. Click the buttons in order to plan your path and minimize total travel distance!

Home (🏡) ➔ A ➔ B ➔ C

Build Your Path:

Your Travel Log: Home ➜ ...

Total Distance: 0.0 miles

Shortest Route: -- miles

🎉 Boom! You optimized the route perfectly to exactly 10.5 miles (Home ➔ A ➔ B ➔ C ➔ Home, or the reverse)! Outstanding pathfinding!