Optimization Problems - Geometric
30 tutor-authored questions for this Ontario curriculum expectation, ordered easiest to hardest, every one with a full worked solution. Work through all 30 with your weekly-lesson access code.
Sample: the first question, solved
"A rectangular garden uses 80m of fencing for all four sides. Using calculus, find the side length that maximizes the area (a square)."
📘 Worked solution
✓Let the sides be w and l with 2w+2l=80, so l=40−w. Area A(w)=w(40−w)=40w−w². A'(w)=40−2w=0 gives w=20, and by symmetry l=20 too - the enclosed square's side is w = 20 m.
And one from the hard end
"An open-top cylindrical can must hold 250cm³. Find the dimensions minimizing surface area (SA=πr²+2πrh)."
Solution shown after you try it in practice mode.
Work through all 30, easiest to hardest
Your Winny Score tracks you as the questions ramp up. Stuck on one? A real Winny Math tutor will walk you through it. First lesson free.
Start practicing