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optimization problems ultimate study guide (area & volume)

You will learn how to solve optimization problems involving areas and volumes for your Calculus 1 class. file:   / 81985426   written solution: https://www.patreon.com/posts/8198561... Thanks to @itsbishop2285 for the timestamps 0:00 Calculus 1 optimization problems (Q1.) 0:35 Find the dimensions of a rectangle with an area of 1000 m2. whose perimeter is as small as possible. (Q2.) 8:35 A farmer has 2400 ft of fencing and wants to fence off a rectangular field that boards a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area? (Q3.) 14:30 The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm2, find the dimensions of the poster with the smallest area. (Q4.) 23:04 Find the dimension of the rectangle of the largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola y=12-x^2 (Q5.) 28:38 A right circular cylinder is inscribed in a sphere of radius 4. Find the largest possible volume of such a cylinder. (Q6.) 42:22 A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross-section) of 90 inches (see figure). Find the dimensions of the package of the maximum volume that can be sent. (Q7.) 47:07 A box with an open top is to be constructed from a square piece of cardboard, 6 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. ** 53:13 The unit should be ft^3 ** (Q8.) 53:21 A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the box that minimize the amount of material used. ----------------------------- Are you loving the math content on my channel and want to see more of it? I'm thrilled to hear that! You can show your support and help me create even better content by becoming a patron on Patreon 👉   / blackpenredpen   or snagging a stylish math shirt or hoodie from my creator store 👉 https://blackpenredpen.creator-spring.... Every bit of support means the world to me and motivates me to keep bringing you the best math lessons out there! So join me on this journey and let's tackle math together! -----------------------------