Question

i posted this problem once before but nobody could answer it, so im gonna try again. can anyone explain how many cases luke has to sell in a month in order to break even on the product?

Luke Corporation produces a variety of products, cach within their own division. Last year, the managers at Luke developed and began marketing a new chewing gum, Bubbs, to sell in vending machines. The product, which sells for $5.15 per case, has not had the market success that managers expected and the company is considering dropping Bubbs. The product-line income statement for the last month follows: S 1,345,180 S Revenue Costs Production costs Product-line margin Allowance for tax (@20%) Product-line profit (loss) $ (1,280,451) 64,729 (12,945.80) $ 51,783.20 Roy O. Andre, the product manager for Bubbs, is concerned about whether the product will be dropped by the company and has employed you as a financial consultant to help with some analysis. In addition to the information given, Mr. Andre provides you with the following data on product costs for Bubbs for the past 12 months: Month Cases Production Costs 211,000 $1,147,828 219,200 1,169,328 216,900 1,177,981 4 232,000 1,193,523 239,900 1,195,827 6 241,000 1,216,673 7 222,200 1,191,699 8 249,200 1,234,774 9 240,800 1,233,226 10 254,600 1,245,325 11 252,200 1,249,760 12 261,200 1,280,451 Assume that the relevant range of production is between 150,000 and 350,000 cases.

Answer 1

Please refer the following image for the solution:  

Breakeven no of cases Luke have to sell in a single month 231046.83 S.no X у 211000 1 2 3 4 5 6 x2 ху 1147828 44521000000 1169328 48048640000 1177981 47045610000 1193523 53824000000 1195827 57552010000 1216673 58081000000 1191699 49372840000 1234774 62100640000 1233226 57984640000 1245325 64821160000 1249760 63604840000 1280451 68225440000 14536395 675181820000 219200 216900 232000 239900 241000 222200 249200 240800 254600 252200 261200 2840200 7 242191708000 256316697600 255504078900 276897336000 286878897300 293218193000 264795517800 307705680800 296960820800 317059745000 315189472000 334453801200 3447171948400 8 9 10 11 12 Total Varaible cost per unit (b) n* (Exy) - (Ex)(Ey) n(Ex?) - (Ex) Fixed cost (a) (Ey) - b(Ex) 12 ΣΧ = Σy = 2x = Exy = 2840200 no. of cases 14536395 production cost 675181820000 3447171948400 Variable cost per unit (b) 12 * (3447171948400) - (2840200) * (14536395) 12 * (675181820000) - (2840200)? 41366063380800 - 41286269079000 8102181840000 - 8066736040000 79794301800 35445800000 $ 3.81 per case Fixed cost (a) 14536395 -3.81 * (2840200) 12 $ 3,715,233 12 $ 309,602.75 Breakeven number of cases Fixed cost / Contribution per unit $309,602.75 / 1.34 231046.83 Fixed cost Contirbution per unit $ 309,602.75 $ 1.34 S Sales Less: Variable cost $ $ 5.15 3.81 1.34