To find how many cameras must be sold to equal the daily costs, we can set up an equation for costs and revenues.
a. How many cameras must the company sell in one day to equal its daily costs?
Let \( x \) be the number of cameras sold in one day.
The total daily costs can be calculated as: \[ \text{Daily Costs} = \text{Overhead Expenses} + \text{Variable Costs} \] \[ \text{Daily Costs} = 1800 + 9x \]
The revenue from selling \( x \) cameras at $18 each is: \[ \text{Revenue} = 18x \]
To break even (i.e., to equal costs and revenues), we set these two expressions equal to each other: \[ 1800 + 9x = 18x \]
Rearranging the equation gives: \[ 1800 = 18x - 9x \] \[ 1800 = 9x \] \[ x = \frac{1800}{9} = 200 \]
Thus, the company must sell 200 cameras per day to equal its daily costs.
b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
If the company increases production by 50 cameras, the new number of cameras sold will be: \[ 200 + 50 = 250 \]
Now, we can calculate the daily revenue from selling 250 cameras: \[ \text{Revenue} = 18 \times 250 = 4500 \]
Next, we calculate the total costs for producing 250 cameras: \[ \text{Costs} = 1800 + 9 \times 250 \] \[ \text{Costs} = 1800 + 2250 = 4050 \]
Now, the daily profit is given by: \[ \text{Profit} = \text{Revenue} - \text{Costs} = 4500 - 4050 = 450 \]
Thus, the daily profit, when increasing production by 50 cameras per day, would be $450.