SOLUTION: Can you please help me solve this problem: a Maufacturer sells a product at $8 per unit, selling all that is produced. Fixed cost is $5000 and variable cost per unit is 22/9 dollar
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Question 99822: Can you please help me solve this problem: a Maufacturer sells a product at $8 per unit, selling all that is produced. Fixed cost is $5000 and variable cost per unit is 22/9 dollars. find the total output and revenue at the break-even point. Find the output required to obtain a profit of $10,000. Could you also please show your work.
Thank you, I most appreciate it
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Manufacturer sells a product at $8 per unit, selling all that is produced. Fixed cost is $5000 and variable cost per unit is 22/9 dollars. find the total output and revenue at the break-even point.
:
Let x = no. of units produced and sold
:
Revenue = 8x
Cost = 5000 + (22/9)x
:
Break-even occurs when Revenue = cost
8x = 5000 + (22/9)x
:
Get rid of the fraction, multiply equation by 9:
9(8x) = 9(5000) + 22x
:
72x = 45000 + 22x
:
72x - 22x = 45000
:
50x = 45000
:
x = 45000/50
:
x = 900 units to break-even
:
:
Check solution by substitution, find out if cost = revenue:
8(900) = $7200
and
5000 + (22/9)900 =
5000 + 2200 = $7200, confirms our solution
:
:
:
Find the output required to obtain a profit of $10,000. Could you also please show your work.
:
Revenue - cost = profit
:
8x - (5000 + (22/9)x) = 10000; find x that will produce this profit
:
8x - 5000 - (22/9)x = 10000
:
8x - (22/9)x = 10000 + 5000
:
8x - (22/9)x = 15000
:
Multiply equation by 9 to get rid of the denominator:
9(8x) - 22x = 9(15000)
:
72x - 22x = 135000
:
50x = 135000
:
x = 135000/50
:
x = 2700 units will produce a 10k profit
:
You should check this solution by substituting 2700 for x in the profit eq:
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