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Optimization | Examples for Calculus 1 | Math with Professor V

Examples in this video: 1. From a thin piece of cardboard 50 in. by 50 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? EDIT: At 13:06 the volume should be 250000/3 (I’m missing a 0 in the video) 2. A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 33 ft3. What dimensions yield the minimum surface area? 3. A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 90 in. What dimensions will give a box with a square end the largest possible volume? 4. A rectangular sheet of perimeter 27 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume? For an introductory video lecture on optimization:    • Calculus 1: Optimization Problems (Se...   Other optimization videos: Larry the Lifeguard:    • Calculus 1: Optimization Example with...   Homework exercises:    • Optimization Problems: Solving Homewo...   Don't forget to LIKE, Comment, & Subscribe! xoxo, Professor V https://linktr.ee/mathwithprofessorv Calculus 2 Lecture Videos on Integration: Integration by parts:    • Calculus 2: Integration by Parts (Vid...   Tabular Integration:    • Integration by Parts - Tabular Method...   Trigonometric integrals:    • Calculus 2: Trigonometric Integrals (...   Trigonometric Substitution:    • Calculus 2: Trigonometric Substitutio...   Partial Fraction Decomposition:    • Calculus 2: Integration of Rational F...   Strategy for Integration:    • Calculus 2: Strategy for Integration ...   Improper Integrals:    • Calculus 2: Improper Integrals (Video...   Trig Review: Unit Circle:    • Trigonometry: Circular Functions (Sec...   Trig Identities:    • Precalculus: Trigonometric Identities...   Sum and Difference Formulas:    • Precalculus: Sum and Difference Formu...   Double Angle & Half-Angle Formulas:    • Precalculus: The Double-Angle and Hal...   Calculus 3 Video Lectures:    • Calculus 3 Video Lectures   #mathwithprofessorv #integration #partialfractions #partialfractionmethod #partialfractiondecomposition #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #calculusvideos #integrationbyparts #integralcalculus Join this channel to get access to perks:    / @mathwithprofessorv   Socials: IG: @mathwithprofessorv TikTok: @mathwithprofessorv I'm also an Amazon influencer, so feel free to support and shop: https://amazon.com/shop/mathwithprofe... EXCITING NEWS: You can now sign up for my Patreon at the link below!   / mathwithprofessorv   My Patreon is a place for students to have access to exclusive ad-free content not available on my YouTube channel! Access to the library of additional videos, worksheets, and more is available with the "Star Pupil Package" tier for just $9.99/month (USD).   / mathwithprofessorv   This video is copy protected and cannot be downloaded or used in any capacity without my permission.