Solving Optimization Word Problems
Read this topicExplanations 10
- Optimization problems focus on finding the best or most effective solutions within everyday life scenarios. The problems presented in calculus often have a focus on maximizing a…
By Emma
- (Video) Optimization of a Perimeter by PatrickJMT Here's a video by patrickJMT showing you how to work through and solve an optimization problem. Optimization problems are, hand…
By Alex Federspiel
- (Video) Optimization Under a Parabola by PatrickJMT The optimization problem he looks at in this video is: Find the dimensions of the rectangle with the largest area that has it…
By Alex Federspiel
- (Video) Optimization of a Rain Gutter by PatrickJMT Here's another video by patrickJMT where he solves an optimization problem in which you have to make a rain gutter. The probl…
By Alex Federspiel
- (Video) Optimization of a Fence by PatrickJMT Here's a video by patrickJMT showing you how to solve yet another optimization problem. This one deals with a perimeter of fencing.…
By Alex Federspiel
- (Video) Optimization of a Box's Volume by PatrickJMT Here's another optimization problem by patrickJMT. This problem deals with the volume of a box. It says, A woman is creating…
By Alex Federspiel
- (Video) Optimization of a Can by PatrickJMT Here's a video by patrickJMT where he hows you how to solve an optimization problem about the volume of a can. The problem states, Su…
By Alex Federspiel
- (Video) Optimization of Two Squares by PatrickJMT Here's a video by patrickJMT going over another optimization problem. The problem states: A 20 inch20\text{ inch}20 inch wire i…
By Alex Federspiel
- (Video) Optimization of a Corridor by PatrickJMT Here's a tricky optimization problem that anyone who's helped a friend move would understand. The problem states: Two corridors …
By Alex Federspiel
- (Video) Optimization of a Rectangle in an Ellipse by PatrickJMT Here's another video by patrickJMT where he finds the optimal rectangle to fit inside an ellipse. The problem sta…
By Alex Federspiel
Problems 11
- What is the largest possible area of a rectangle with side lengths 10sinx10\sin{x}10sinx and 10cosx10\cos{x}10cosx for some real xxx? Source: HMMT February 1999
- We need to build a box in the shape of a rectangular prism with a square base and an open top. Given that we have only 12 square feet of cardboard, what is the maximum volume th…
- We want to build a cylindrical tube with no top (one end sealed, the other open) using 12π in312\pi \ {\rm in}^312π in3 of cardboard. Find the height of the tube (in inches) tha…
- A rectangular poster of area 54 in254 \ \textrm{in}^254 in2 has 111-inch blank margins on the bottom and sides, and a 222-inch blank margin on top. Find the largest printed area…
- Find the xxx-coordinate of the point on the curve y=xy = \sqrt xy=x that is closest to the point (4,0)(4,0)(4,0).
- What is the largest volume of the circular cone that can be built out of a cardboard with area 18π18\pi18π? Round to the nearest integer, without units.
- Find two numbers whose difference is 200200200 and whose product is a minimum.
- Farmer Grace is building a pen for her alpacas. The pen is built by the river to save on fencing (the alpacas won't swim away). Furthermore, she wants to split the pen into four…
- You're creating a secret room behind a bookcase for your new mansion. The room is to have a volume of 800 ft3800\text{ ft}^3800 ft3. The width of the base of the room is to be f…
- A right circular cylinder is inscribed in a sphere of radius RRR. What is the largest possible volume of such a cylinder.
- If her manager asks her to select a single, continuous 444-hour shift between 111111 AM and 111111 PM, what shift should she select to maximize the amount of tables that are occ…