How to set up optimization problems (20 common calculus 1 questions)

Get the file:   / how-to-set-up-20-169957520   Most students don't fail optimization on the calculus, they fail on the setup. Translating word problems into a single, solvable function is the ultimate bottleneck in Calculus 1. I worked through 20 optimization problems to cover every primary setup pattern you will encounter on an exam: 1. Distance minimization 2.Area and perimeter constraints 3.Cost and revenue optimization 4.Trigonometric setup models Shop my math t-shirts & hoodies: https://amzn.to/3qBeuw6 ----- This channel is dedicated to sharing the fun of mathematics and inspiring students around the world. Thank you to these Patreon members for building this with me. 3Blue1Brown • Allison Lamery • Anthony Hunting • Anyway • Ben Delo • Caoimhe Seymour • charlie lewinski • Corey Rufener • CTAR • David I Miller • Doc Ockey • exchsac • Gramps • Hayden S • huguens nevelus • jappiesaus • Jessica • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Michael ZHOU • Michelle Liang • Mister Hardware • Mizel Cluett • Nerd • Nicolai Lilly • Ricardo Murillo • Rohan • SaltyFishbutwithDream • Sebastian Correa • Sharnay Ampos • Steven McEwan • Subotai Baghatur • Terry Chang • Tomaz Mevlja • Torbjörn Karlsson • Whoever • Zero • Zhansu (Updated: September 2026   / blackpenredpen  ) #blackpenredpen #math #mathtutorials ----- 0:00 Intro Q1, 0:53, Two numbers with difference 40 and minimum product Q2, 4:15, Two positive numbers with product 100 and minimum sum Q3, 6:18, Closest point on y=sqrt(x) to (4,0) Q4, 9:42, Angle theta to minimize pulling force Q5, 12:19, Production level to maximize total profit Q6, 18:00, Rectangular garden with wire mesh and stone wall (min cost) Q7, 22:54, Theater ticket price to maximize revenue Q8, 28:42, Open-top box from a 10x16 cardboard sheet Q9, 34:08, Postal box with square base (max volume, length+girth=108) Q10, 38:08, Closed box with square base and fixed volume (min surface area) Q11, 42:45, Open-top cylindrical container (min surface area) Q12, 48:47, Closed cylindrical can with fixed surface area (max volume) Q13, 51:57, Poster dimensions with top/bottom and side margins (min total area) Q14, 56:11, Largest rectangle inscribed in an ellipse Q15, 1:02:52, Rectangle under the curve y=e^(-x^2) Q16, 1:06:13, Cylinder inscribed in a cone Q17, 1:13:11, Norman window with fixed perimeter (max area) Q18, 1:16:57, Rowing boat to shore (minimize travel time) Q19, 1:25:00, Minimum length ladder reaching over a fence to a building Q20, 1:31:43, Maximize the angle between wires from two poles