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

## Step 1: Understand 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: Calculate Possible Combinations<br />### We need to find combinations of movies and gym sessions that sum up to 4 activities in total, as this is the maximum he can afford with his budget.<br /><br />## Step 3: Evaluate Utility for Each Combination<br />### For each combination of movies and gym sessions, calculate the total utility by adding the utility from movies and the utility from gym sessions:<br /><br />- **0 Movies, 4 Gym Sessions**: Total Utility = 0 (Movies) + 107 (Gym) = 107<br />- **1 Movie, 3 Gym Sessions**: Total Utility = 30 (Movies) + 115 (Gym) = 145<br />- **2 Movies, 2 Gym Sessions**: Total Utility = 55 (Movies) + 85 (Gym) = 140<br />- **3 Movies, 1 Gym Session**: Total Utility = 76 (Movies) + 50 (Gym) = 126<br />- **4 Movies, 0 Gym Sessions**: Total Utility = 92 (Movies) + 0 (Gym) = 92<br /><br />## Step 4: Determine the Maximum Utility<br />### Compare the total utilities calculated for each combination. The combination with the highest total utility is the utility maximizing point.