A camera manufacturer spends $1750 each day for overhead expenses plus $6 per camera for labor and materials. The cameras sell for $16 each. How many cameras must the company sell in one day to equal its daily costs? If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
a
The company must sell 110 cameras to equal its daily costs; $150
b
The company must sell 175 cameras to equal its daily costs; $500
c
The company must sell 105 cameras to equal its daily costs; $200
d
The company must sell 175 cameras to equal its daily costs; $800
To calculate the number of cameras the company must sell to equal its daily costs, we need to set up an equation.
Let x be the number of cameras the company must sell.
The total cost for the company is $1750 + $6x
The total revenue for the company is $16x
To find the number of cameras the company must sell to equal its daily costs, we set the total cost equal to the total revenue:
1750 + 6x = 16x
1750 = 10x
x = 175
So, the company must sell 175 cameras to equal its daily costs.
To calculate the daily profit if the company can increase production by 50 cameras per day, we consider the new total revenue with the increased production:
New total revenue = $16(x + 50)
Now we can calculate the new daily profit:
New daily profit = New total revenue - Total costs
New daily profit = $16(x + 50) - (1750 + 6x)
New daily profit = $16(175 + 50) - (1750 + 6*175)
New daily profit = $16(225) - (1750 + 1050)
New daily profit = $3600 - 2800
New daily profit = $800
Therefore, if the company can increase production by 50 cameras per day, their daily profit would be $800.
The correct answer is d) The company must sell 175 cameras to equal its daily costs; $800.