Here is my Alzheimer's problem of the day.
I hastily graphed the reaction functions and found 50 for non-OPEC and 65 for OPEC. Direct computation yeilds a price of $26 2/3. The profit is equal to PQ - TC. Profit equals $1408 1/3. Non-OPEC equals $833 1/3.
I loved working this problem. I can't believe the amount of trouble I had with fractions. I am always amazed how the basics seem to disappear when the level of difficulty increases. The question I have for educators is "what level of rigor is needed for learning?" What I mean is should teachers make the problems so hard that students must take hours to solve the problem or show the work be easy so that a lot more ground can be covered?