Suppose in the Stanford Stadium problem that $10\%$ of the General Public would use false pretenses $($counterfeit or borrowed student ID$)$ to buy a student ticket. Stanford knows this. Assume the same initial response functions we used in class, and assume the willingness to pay distribution for cheaters is the same as non$-$cheaters $($i$.$e$.,$ uniform$).($Hint: Build three response functions: $($a$)$ students, $($b$)$ General Public cheaters, $($c$)$ General Public non$-$cheaters.$)$

Write out the correct optimization formulation for this problem. Use p$\_$s for the student price, p$\_$g for the general public price.

How should Stanford set their General Public and Student prices? $($solve for optimal prices in Excel$)$

What are the new optimal revenues?

How many of the student ticket sales are to $$real$$ students and how many are to $$fake$$ students?