No one can solve this!! if you solve this, your a genius! 10 points!?
Question by mamz123: No one can solve this!! if you solve this, your a genius! 10 points!?
An electronics firm manufactures portable DVD players, receiving $ 120 for each unit it makes. If x represents the number of units produced, the income received is determined by the revenue funtion R(x)=120x. The manufacturer has fixed costs of $ 12, 000 per month and variable costs of $ 57.50 for each unit manufactured. Thus, the cost function is C(x)= 57.50x + 12,000. How many DVD players must the company sell for revenue to equal cost?
**Please answer correctly, and show steps! Thanks!
Best answer:
Answer by MEgAmaan
easy 2
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The answer is 245
How?
12 + 12 + 200 + 21= 245
SIMPLE and EASY TO UNDERSTAND!
Do not ask such easy questions again.
x = 12,000 / 62.5
$ 120x+$ 12000=Cx
Set the revenue function equal to the cost function and solve for x
R(x) = C(x)
120x = 57.50x + 12,000
62.5x = 12,000
x = 12,000/62.5
x = 192
They need to sell 192 DVD players for revenue to equal cost.
to break even the company must sell 192 dvd players. it works best if you use a graphing calculator. you have to consider that even though they bring in $ 120 for each unit, $ 57.50 is lost in cost of production. so truly their net gain is $ 62.50 per unit. $ 12000 is the amount they need to sell in order to cover their costs alone. so if you graph a horizontal line of y=12000 and the revenue line of y=62.5x and find the intersection point, you will see that it takes 192 dvd players to bring in $ 12000.
hooray for being a genius :)
120x= 57.50x+12,000
62.5x/62.5=12,000/62.5
x=192
to check:
120(192)= 57.50(192)+12,000
23,040=11,040+12,000
23,040=23,040
Monthly break-even units of production and sales (x):
$ 120.00x = $ 12,000.00 + $ 57.50x
$ 62.50x = $ 12,000.00
x = 192
Answer: 192 units
Proof (Revenue less expenses = no income no loss, $ 0.00)
= (192 units[$ 120.00]) – ($ 12,000.00 + 192 unit[$ 57.50])
= $ 23,040.00 – ($ 12,000.00 + $ 11,040.00)
= $ 23,040.00 – ($ 23,040.00)
= $ 23,040.00 – $ 23,040.00
= $ 0.00
Another way is by contribution margin:
Formula:
= fixed cost/(price per unit – variable cost per unit)
Applied:
= $ 12,000.00/($ 120.00 – $ 57.50)
= $ 12,000.00/$ 62.50
= 192