....and why not "Jeg trenger åpne butikken"?
Why "åpne" and not "åpen"?
'åpen' is the adjective, 'åpne' is the verb.
Would this refer to opening it for the day, or a grand opening?
"Let's open the store for the day" versus "I want to open a store someday"
It's "butikken" which is specifically THE shop, so it would be the former.