A fitness center offers several membership packages

Question

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.

catinabox · Answer

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 .

Bismuth83 · Answer

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  .

Bunuel · Answer

IMPROVED VERSION OF THIS QUESTION IS HERE: the-table-below-outlines-the-annual-membership-plans-available-443797.html

A fitness center offers several membership packages

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