7. Party-goers of Chicago enjoy going to music clubs (a.k.a. "warehouses") to listen and dance to electronic music, primarily House music. The question club managers face is to determine i) how much to invest in club facilities, G - the quality of sound system, size of the dance floor, radius of the disco ball, etc. -, and the number of partygoers to have in each club, N. Each party-goer also enjoys a private consumption good, r (drinks, clothes, lights, etc.). Preferences are represented by the utility function U = x +201/2 + N _ N' 400 Each partygoer has a party budget of $1,000. Assuming that club costs are split equally, so that the budget constraint per person is given by 1000 = s + N (Assume that the population of Chicago is very large relative to / so that integer problems are not a concern) a) Substitute in the budget constraint into the utility function so that U is expressed in terms of G and N