Bob budgets 12 a week for entertainment. He splits his time between going to the movies and going to the gym. Each movie costs 3 and each session at the gym also costs 3 . The total utility from each of these activities is shown in the table below. Bob's utility maximizing point is: Movies & Total Utility & Gym Costs & Total Utility 0 & 0 & 0 & 0 1 & 30 & 1 & 50 2 & 55 & 2 & 85 3 & 76 & 3 & 115 4 & 92 & 4 & 107 5 & 103 & 5 & 111 & & 6 & 114 & & 7 & 115 4 movies; 2 gym workout sessions 3 movies; 3 gym workout sessions 4 movies; 0 gym workout sessions 1 movie: 5 gym workout sessions

## Step 1: Understanding the Budget Constraint<br />### Bob has a budget of $12 for entertainment. Each movie and gym session costs $3. Therefore, the total number of activities (movies + gym sessions) he can afford is $\frac{12}{3} = 4$.<br /><br />## Step 2: Calculating Total Utility for Each Option<br />### We need to calculate the total utility for each combination of movies and gym sessions that fits within the budget constraint:<br /><br />- **Option 1: 4 movies; 2 gym workout sessions**<br /> - Cost: \(4 \times 3 + 2 \times 3 = 12\)<br /> - Total Utility: 92 (from movies) + 85 (from gym) = 177<br /><br />- **Option 2: 3 movies; 3 gym workout sessions**<br /> - Cost: \(3 \times 3 + 3 \times 3 = 12\)<br /> - Total Utility: 76 (from movies) + 115 (from gym) = 191<br /><br />- **Option 3: 4 movies; 0 gym workout sessions**<br /> - Cost: \(4 \times 3 + 0 \times 3 = 12\)<br /> - Total Utility: 92 (from movies) + 0 (from gym) = 92<br /><br />- **Option 4: 1 movie; 5 gym workout sessions**<br /> - Cost: \(1 \times 3 + 5 \times 3 = 18\) (Exceeds budget, not feasible)<br /><br />## Step 3: Determining the Utility Maximizing Point<br />### Among the feasible options, we compare the total utilities:<br />- Option 1: 177<br />- Option 2: 191<br />- Option 3: 92<br /><br />### The highest total utility is 191, which corresponds to Option 2: 3 movies and 3 gym workout sessions.