Optimization
By DarthVader
Date: 2022-08-16
Topic: 157 see comments
Post views: 1054
Optimization Problems
Here are some steps for solving a soda can optimization problem using differentiation:
Video: https://youtu.be/lx8RcYcYVuU
Step 1:
Define the ‘objective’.
This is the equation for whatever quantity needs to be maximised, or minimised.
E.G. volume, surface area
Step 2:
Define the ‘constraint’.
This is the equation for whatever quantity or value needs to remain constant and unchanged.
Goal:
The goal is to take the first derivative of the ‘objective equation’ and set it equal to zero then solve for ‘x’ or ‘y’ (can be any variable).
Step 3:
Solve the constraint equation for one of its variables so that you can substitute that into the objective equation.
This is so that you can get the objective quantity that is to be minimised/maximised, so that it is in terms of one other variable. So by substituting a variable from the second equation into the first, you effectively eliminate one variable, and this is in order to take the derivative of the ‘objective’ equation.
Step 4:
Take the derivative of the objective equation and then set it equal to zero.
Next solve the equation and then find the stationary/critical points.
Step 5:
Test if the stationary/critical points are a local maximum or minimum.
If the problem is a minimisation problem then you need to find a local minimum, likewise if the problem is a maximisation problem you need to find a local maximum.
Step 6:
Plug in the remaining variable calculated in step 4 into the original equation to find the y-value.
Comments | Creator | Date | ID |
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Tricky :| |