# Profit Calculation for a Dog Grooming Business

## Logan and Berkeley's Dog Grooming Business

**Logan and Berkeley have a thriving dog grooming business that operates for 5 hours a day, 4 days a week. They are considering hiring a second dog groomer to expand their business. They believe that the new groomer will be able to groom 3 dogs per hour after a 12-week period. However, during the first 12 weeks, the new groomer will only be able to groom 1 dog per hour as they learn the ropes.**

### The Challenge

**Logan and Berkeley are faced with the decision of hiring a second groomer, which would require installing an additional sink costing $20,000 and incurring an additional $27 per hour in labor costs. Their current expenses include $15 per dog groom for items such as dog shampoo and $30,000 in fixed costs per year (e.g. rent). They charge $50 per dog groom.**

## How many weeks does it take for the second groomer to pay off and make a profit?

### Calculating the Total Costs

Costs associated with hiring a new employee include:

- $20,000 (new sink) + $27 per hour + $15 per dog groom

Now, let's calculate the total costs per week:

#### First 12 Weeks:

- $20,000 (new sink) + $540 per week + $300 (grooming 20 dogs) = $20,840

#### After 12 Weeks:

- $20,000 (new sink) + $540 per week + $900 (grooming 60 dogs) = $21,440

### Calculating the Total Profit

- $35 per dog
- First 12 weeks: $700
- After 12 weeks: $2100

Finally, calculate the time it takes for the new employee to start making a profit:

- Profit during the first 12 weeks: $8,400
- Costs during the first 12 weeks: $20,840 + $10,080
- Total balance: $21,920 - $8,400 = $13,520

#### Profit after the First Twelve Weeks:

- Profits per week: $2100
- Costs: $13,520 + $1,440 per week

#### After 20 Weeks:

- Profits per week: $42,000
- Costs: $13,520 + $28,800 = $42,320
- Total balance: $42,320 - $42,000 = $300

This means that by the end of week 32, the employee has almost paid off all the costs, and it is expected by week 33, they can start making a profit.

How many weeks does it take for the second groomer to pay off and start making a profit? The number of weeks it will take for the new employee to start making a profit is 33 weeks.