You will learn how to solve optimization problems involving areas and volumes for your Calculus 1 class.
file: / 81985426
written solution: 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.
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