To determine how many cameras the company must sell to equal its daily costs, let's first calculate the total daily costs.
Given:
- Daily overhead costs = $1,800
- Cost per camera (labor and materials) = $9
- Selling price per camera = $18
Part a: Calculate the number of cameras to break even
Let \( x \) be the number of cameras sold in one day.
The total daily costs can be determined as follows: \[ \text{Total Costs} = \text{Overhead Costs} + \text{Cost per Camera} \times \text{Number of Cameras} \] \[ \text{Total Costs} = 1,800 + 9x \]
The total revenue from selling \( x \) cameras is: \[ \text{Total Revenue} = \text{Selling Price per Camera} \times \text{Number of Cameras} \] \[ \text{Total Revenue} = 18x \]
To find the break-even point, we set the total costs equal to the total revenue: \[ 1,800 + 9x = 18x \]
Now, solve for \( x \): \[ 1,800 = 18x - 9x \] \[ 1,800 = 9x \] \[ x = \frac{1,800}{9} = 200 \]
Answer to part a: The company must sell 200 cameras in one day to equal its daily costs.
Part b: Calculate the daily profit if production is increased
If the manufacturer can increase production by 50 cameras, the new number of cameras sold per day will be: \[ x + 50 = 200 + 50 = 250 \]
Now we will calculate the total revenue and total costs for the sale of 250 cameras.
Total Revenue for 250 cameras: \[ \text{Total Revenue} = 18 \times 250 = 4,500 \]
Total Costs for 250 cameras: \[ \text{Total Costs} = 1,800 + 9 \times 250 \] \[ \text{Total Costs} = 1,800 + 2,250 = 4,050 \]
Daily Profit can be calculated as: \[ \text{Profit} = \text{Total Revenue} - \text{Total Costs} \] \[ \text{Profit} = 4,500 - 4,050 = 450 \]
Answer to part b: Their daily profit would be $450.
1 answer