A stock price is currently $$23.$ A reverse $($i$.$e$.$ short$)$ butterfly spread is created

from put options with strike prices of $$20,$ $$25,$ and $$30.$ The costs of the puts

are $$1$ for $$20$ put, $$3$ for $$25$ put, and $$5\mathrm{.}5$ for $$30$ put. Use graphs to illustrate

the profit pattern of this spread. What are the maximum gains and maximum

losses from the spread?