Fixed cost are 4500 per month. Variable cost per mug is 5 and the company sells each mug for 10. If the company aims to make a monthly profit of 1000, how many mugs must they sell?

Let x be the number of mugs the company must sell to make a monthly profit of 1000.

Total cost = Fixed cost + Variable cost
Total cost = 4500 + 5x

Total revenue = Selling price per mug * Number of mugs sold
Total revenue = 10x

Profit = Total revenue - Total cost
1000 = 10x - (4500 + 5x)
1000 = 10x - 4500 - 5x
1000 = 5x - 4500
5x = 5500
x = 1100

Therefore, the company must sell 1100 mugs to make a monthly profit of 1000.

Let's denote the number of mugs sold as "x".

1. Calculate the total revenue:
Total revenue = Selling price per mug - Number of mugs sold
Total revenue = 10 - x

2. Calculate the total variable cost:
Total variable cost = Variable cost per mug - Number of mugs sold
Total variable cost = 5 - x

3. Calculate the total cost:
Total cost = Fixed cost + Total variable cost
Total cost = 4500 + 5 - x

4. Calculate the profit:
Profit = Total revenue - Total cost
Profit = 10 - x - (4500 + 5 - x)

5. Set the profit equal to the target profit of 1000:
10 - x - (4500 + 5 - x) = 1000

6. Solve for "x":
5 - x - 4500 = 1000
5 - x = 5500
x = 5500 / 5
x = 1100 mugs

Therefore, the company must sell 1100 mugs to achieve a monthly profit of 1000.