Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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 capital-intensive, 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 break-even 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 / p-c, 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 break-even 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: 2,505 Thanks: 1374 $c_1(n) = 46400+720n$ $c_2(n) = 400100 + 210n$ 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: 6,788 Thanks: 708 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!  Tags analysis, break, simple ### What is the break-even quantity beyond which the second process becomes more attractive than the first

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