Since , so
To find the quantity that maximizes revenue , set . This gives , calculate and use it to calculate the corresponding revenue . Check that it really is a maximum.
c) Profit is equal to total revenue minus total cost . To find the maximum profit with respect to quantity sold , set
. You get
, find (discard negative solution)
and use it to calculate corresponding profit . Check that it really is a maximum.
Maybe I forgot to multiply by 1000 somewhere but I hope you get the idea.