
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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August 28th, 2017, 12:16 PM  #1 
Member Joined: Sep 2010 From: Europe Posts: 45 Thanks: 1  Simple break even analysis
Hello. I have this task saying: “Two different manufacturing processes are being considered for making a new product. The first process is less capitalintensive, with fixed costs of only 46400$ per year and variable costs of 720$ per unit. The second process has fixed costs of 400100$ but has variable costs of only 210$ per unit. a) What is the breakeven quantity, beyond which the second process becomes more attractive than the first? b) If the expected annual sale for the product is 840 units, which process would you choose? " I think I know the formula for a break even analysis. I think it is Q = F / pc, where F = fixed cost, p = price and c = variable costs. My book says so since "we set total revenue equal to total cost, we get the breakeven quantity point as pQ = F + cQ (p  c)Q = F Q = F / p  c Now, to question a). I need to find the Q. But, I do not have the p. What should I do? In advance, Thank you very much Kind regards, Pumaftw 
August 28th, 2017, 12:49 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 
$c_1(n) = 46400+720n$ $c_2(n) = 400100 + 210n$ the break even quantity occurs when the cost of producing $N$ items becomes cheaper for the 2nd process. $c_1(N)>c_2(N)$ $46400 + 720N >400100+210N$ $510N >353700$ $N > 693.529$ so we would say $N=693$, as we can only produce integer quantities. at $N>693$ process 2 becomes cheaper b) Since you expect to sell 840>693 units you would want to use process 2. 
August 28th, 2017, 12:50 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,511 Thanks: 585 
Let x be number of units. 46400+720x is first process cost. 400100+210x is second process cost. Break even is x where they are equal. 
August 29th, 2017, 12:57 AM  #4 
Member Joined: Sep 2010 From: Europe Posts: 45 Thanks: 1 
Thank you both for fast response. I wasn't all that wrong in my notes, I was somewhat in the right direction. Again, thank you! 

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