What is the total utility of the combination of going to the nightclub 3 times per month and the cinema 2 times per month? What combination of the two activities maximizes Ozzie's satisfaction?

From the table, for 3 visits to a nightclub, Total Utility (TU) = 240.

From the table, for 2 visits to the cinema, Total Utility (TU) = 110.

The total utility for this combination is $\boxed{350}$.

Marginal Utility (MU) is the change in Total Utility (TU) from consuming one more unit.

For nightclubs: MU_N/P_N = MU_N / \20$For cinema:$MU_C/P_C = MU_C / $10$

Here is the completed table with MU and MU/P values:

• 1st purchase: Cinema (1st visit) gives 6.0 MU/$. Cost:$$10$. Budget remaining:$$90$.
• 2nd purchase: Cinema (2nd visit) gives 5.0 MU/$. Cost:$$10$. Budget remaining:$$80$.
• 3rd purchase: Nightclub (1st visit) gives 5.0 MU/$. Cost:$$20$. Budget remaining:$$60$.
• 4th purchase: Cinema (3rd visit) gives 4.0 MU/$. Cost:$$10$. Budget remaining:$$50$.
• 5th purchase: Nightclub (2nd visit) gives 4.0 MU/$. Cost:$$20$. Budget remaining:$$30$.
• 6th purchase: Cinema (4th visit) gives 3.0 MU/$. Cost:$$10$. Budget remaining:$$20$.
• 7th purchase: Nightclub (3rd visit) gives 3.0 MU/$. Cost:$$20$. Budget remaining:$$0$.

At this point, Ozzie has purchased:

• 3 nightclub visits: 3 \times \20 = $60$
• 4 cinema visits: 4 \times \10 = $40$Total expenditure =$$60 + $40 = $100$. This matches the budget. At this combination, the last unit of nightclub consumed yielded 3.0 MU/$ and the last unit of cinema consumed yielded 3.0 MU/$. The equimarginal principle is satisfied.

The combination that maximizes Ozzie's satisfaction is $\boxed{\text{3 nightclub visits and 4 cinema visits}}$.