A clarinet factory wants to maximize profits. They can produce 250 clarinets per week at a cost of $300 per clarinet, and sell them for $1000 per clarinet.
And, they can produce 350 clarinets per week at a cost of $275 per clarinet, and sell them for $900 each.
How much profit can they expect to earn if they make 400 clarinets per week?
To calculate the profit, we need to subtract the cost of production from the revenue obtained from selling the clarinets.
The first step is to calculate the cost of producing 400 clarinets per week using the given information.
For the option of producing 250 clarinets per week at a cost of $300 per clarinet:
The total cost of producing 400 clarinets per week can be calculated using the formula (cost per clarinet x number of clarinets produced):
Cost of producing 400 clarinets = $300 x 400 = $120,000
For the option of producing 350 clarinets per week at a cost of $275 per clarinet:
The total cost of producing 400 clarinets per week:
Since the factory can only produce a maximum of 350 clarinets per week, we need to calculate the cost of producing 350 clarinets and then find the cost of producing the additional 50 clarinets:
Cost of producing 350 clarinets = $275 x 350 = $96,250
Cost of producing the additional 50 clarinets = ($275 x 50 = $13,750)
Total cost of producing 400 clarinets = $96,250 + $13,750 = $110,000
Now that we have calculated the cost, we can calculate the profit for each case.
Option 1: Producing 400 clarinets per week with a cost of $120,000
Revenue obtained from selling 400 clarinets at $1000 per clarinet = $400,000
Profit = Revenue - Cost = $400,000 - $120,000 = $280,000
Option 2: Producing 400 clarinets per week with a cost of $110,000
Revenue obtained from selling 400 clarinets at $900 per clarinet = $360,000
Profit = Revenue - Cost = $360,000 - $110,000 = $250,000
Therefore, the factory can expect to earn a profit of $280,000 by producing 400 clarinets per week in option 1, and a profit of $250,000 in option 2.