A camera manufacturer spends $2050 each day for overhead expenses plus $7 per camera for labor and materials. The camera sells for $17 each.
a. How many cameras must the company sell in one 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 cost = revenue for x cameras, then
2050+7x = 17x
x=205
Assuming you mean 50 more than the break-even number, then since profit = revenue - cost,
p = 17*255 - (2050+7*255)
Another way to look at it is that the profit per camera is 17-7=10 dollars.
So, with zero profit at 205 units, all the profit made on the extra 50 cameras is 50*10 = $500
To answer these questions, we need to calculate the daily costs and the daily profit of the camera manufacturer.
a. To determine how many cameras the company must sell in one day to equal its daily costs, we'll first calculate the daily costs and then divide it by the selling price of each camera.
Daily costs = Overhead expenses + (Labor and materials per camera * Number of cameras)
Daily costs = $2050 + ($7 * Number of cameras)
To break even, the company needs to sell enough cameras to cover its daily costs. So, we set the daily costs equal to the revenue from selling the cameras:
Daily costs = Number of cameras * Selling price per camera
$2050 + ($7 * Number of cameras) = Number of cameras * $17
Now, we can solve this equation to find the number of cameras the company must sell:
$2050 + ($7 * Number of cameras) = Number of cameras * $17
Let's simplify the equation:
$2050 + $7 * Number of cameras = $17 * Number of cameras
$2050 = $17 * Number of cameras - $7 * Number of cameras
$2050 = $10 * Number of cameras
Number of cameras = $2050 / $10
Number of cameras = 205
Therefore, the company must sell 205 cameras in one day to equal its daily costs.
b. To calculate the daily profit with an increased production of 50 cameras per day, we'll calculate the revenue from selling the cameras and subtract the daily costs:
Daily revenue = Number of cameras * Selling price per camera
Daily costs = $2050 + ($7 * Number of cameras)
Daily profit = Daily revenue - Daily costs
Daily profit = (Number of cameras + 50) * $17 - ($2050 + ($7 * (Number of cameras + 50)))
Let's substitute the value of the original number of cameras:
Daily profit = (205 + 50) * $17 - ($2050 + ($7 * (205 + 50)))
Now, we can calculate the daily profit:
Daily profit = (255) * $17 - ($2050 + ($7 * (255)))
Thus, the manufacturer's daily profit with an increased production of 50 cameras per day can be calculated by substituting the above expression and solving it.