A fitness center offers several membership packages, each with different pricing and benefits. A member can either pay a one-time fee for an annual membership they prefer and pay extra for add-ons. The membership packages are as follows: 1. Basic Plan: $100 per year with access to all standard equipment and group classes. 2. Silver Plan: $200 per year with access to all standard equipment, group classes, and a 10% discount on personal training sessions. 3. Gold Plan: $300 per year with access to all standard equipment, group classes, a 20% discount on personal training sessions, and two free personal training sessions. 4. Platinum Plan: $450 per year with access to all standard equipment, group classes, a 30% discount on personal training sessions, and five free personal training sessions. Personal Training sessions cost $80 per session.Three friends decide to enroll at the fitness center for a year. During that time, they plan to take the following activities at the gym: https://gmatclub.com/forum/download/file.php?id=78391The gym has analyzed the number of members enrolled in each of the tiers along with the revenue from personal training sessions and found the following information: https://gmatclub.com/forum/download/file.php?id=78392 IMPROVED VERSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-table-be ... 43797.html gym2.png gym1.png

Official Solutions: Q1. Which plan is most advantageous for Sally? Cost calculation for each plan: Basic Plan : Cost: $100 per year Personal training sessions: 5 × $80 = $400 Total cost : $100 + $400 = $500 Silver Plan (10% discount on personal training): Cost: $200 per year Personal training sessions: 5 × $80 × 0.9 = $360 Total cost : $200 + $360 = $560 Gold Plan (20% discount on personal training and 2 free sessions): Cost: $300 per year Free sessions: 2 Paid sessions: 3 × $80 × 0.8 = $192 Total cost : $300 + $192 = $492 Platinum Plan (30% discount on personal training and 5 free sessions): Cost: $450 per year Free sessions: 5 (covers all sessions) Total cost : $450 The Platinum Plan offers the lowest total cost for Sally at $450 , making it the most advantageous option for her. Q2. Which plan is most advantageous for Mindy? Cost calculation for each plan: Basic Plan : Membership cost: $100 per year Personal training sessions: 10 × $80 = $800 Total cost : $100 + $800 = $900 Silver Plan (10% discount on personal training): Membership cost: $200 per year Personal training sessions: 10 × $80 × 0.9 = $720 Total cost : $200 + $720 = $920 Gold Plan (20% discount on personal training and 2 free sessions): Membership cost: $300 per year Free personal training sessions: 2 Paid sessions: 8 × $80 × 0.8 = $512 Total cost : $300 + $512 = $812 Platinum Plan (30% discount on personal training and 5 free sessions): Membership cost: $450 per year Free personal training sessions: 5 Paid sessions: 5 × $80 × 0.7 = $280 Total cost : $450 + $280 = $730 The Platinum Plan is the most advantageous for Mindy, with a total cost of $730 . Q3. Which tier generates the most revenue for the gym? Calculation for total revenue (membership fees + personal training revenue) for each tier: Basic : Membership revenue: 1,500 × $100 = $150,000 Personal training revenue: $40,000 Total: $150,000 + $40,000 = $190,000 Silver : Membership revenue: 200 × $200 = $40,000 Personal training revenue: $72,000 Total: $40,000 + $72,000 = $112,000 Gold : Membership revenue: 100 × $300 = $30,000 Personal training revenue: $80,000 Total: $30,000 + $80,000 = $110,000 Platinum : Membership revenue: 60 × $450 = $27,000 Personal training revenue: $140,000 Total: $27,000 + $140,000 = $167,000 The Basic tier generates the most total revenue at $190,000 .

1. Part 1. The question asks us to figure out which plan is better for Sally . 2. Group classes preference is not important since all plans offer it. Sally will take 5 personal training sessions. Then her total cost for a plan will be equal to Annual Cost + $80 * Discount * (# of personal training sessions - # of free sessions). Now let's look at the potential costs: - Basic: $100 + $80 * 1 * (5 - 0) = $500. - Silver: $200 + $80 * 0.9 * (5 - 0) = $560. - Gold: $300 + $80 * 0.8 * (5 - 2) = $492. - Platinum: $450 + $80 * 0.7 * (5 - 5) = $450. In this case, Platinum is the best plan for Sally . 3. Part 2. The question asks us to figure out which plan is better for Mindy . 4. Group classes preference is not important since all plans offer it. Mindy will take 10 personal training sessions. Then her total cost for a plan will be equal to Annual Cost + $80 * Discount * (# of personal training sessions - # of free sessions). Now let's look at the potential costs: - Basic: $100 + $80 * 1 * (10 - 0) = $900. - Silver: $200 + $80 * 0.9 * (10 - 0) = $920. - Gold: $300 + $80 * 0.8 * (10 - 2) = $812. - Platinum: $450 + $80 * 0.7 * (10 - 5) = $730. In this case, Platinum is the best plan for Mindy . 5. Part 3. We need to find the tier that generates the most revenue for the gym . This is equal to # of members * Annual Cost + Revenue from Personal Training Sessions. Now, let's calculate for each tier: - Basic: 1500 * $100 + $40000 = $190000. - Silver: 200 * $100 + $72000 = $92000. - Gold: 100 * $100 + $80000 = $90000. - Platinum: 60 * $100 + $140000 = $146000. So, the tier that generates the most revenue is Basic .