Utility maximizationQuestion $2$

Consider an actor whose latest show has just become a "breakthrough hit." The

actor makes choices about how much time to spend engaging with celebrity

spotters on the street $($S$)$ and with people who "slide into his DMs$"($direct

messages, or D$)$ on social media. These can benefit an actor's career and ego, but

can too much be a bad thing? The actor's problem is:

maxu$(S,D)=(S-5{)}^2+(D-5{)}^2$

subject $toS(D)=\sqrt[\phantom{2}]{(25-D^2)}$

a$.$ What should go under the max sign above, and why?

b$.$ Using a set of axes with Spottings on the $y-$axis and DMs on the $x-$axis, explain

the shape of the actor's feasibility frontier.