Question

Exercise 4.26 Pearl developed an innovative computer game, called Home By Myself (HBM). It was so successful that she quickly followed up with two sequels: Home By Myself II (HBM2) and Home By Myself III (HBM3). The costs of developing the games were $88,000 for HBM, $6,000 for HBM2, and $14,500 for HBM3. The production process consists of using her computer to copy the games to blank DVDs and then packing them with printed instructions in a display box. It takes longer to copy the original game than it takes to copy the sequels. Pearl can produce, ready for shipping, about 20 copies of HBM, 30 copies of HBM2, or 45 copies of HBM3 in an hour, and she normally works 8 hours per day. HBM HBM2 HBM3 Selling price $ 48.00 $ 28.30 $ 28.30 Costs Blank DVD 1.20 0.70 0.70 Instructions and packaging 3.80 1.80 1.80 Prorated development costs* 17.60 1.20 2.90 Margin $ 25.40 $ 24.60 $ 22.90 Daily demand 120 games 120 games 90 games *The prorated development costs were determined for each game by dividing the game’s development costs by 5,000, the estimated minimum total demand for each game. What is the contribution margin per hour of Pearl’s time for each game? (Round all entries to 2 decimal places, e.g. 5.35.) HBM HBM2 HBM3 Contribution margin per hour: $ $ $ In what order should Pearl produce the games? Production order: HBM3, then HBM, and then HBM2HBM2, then HBM3, and then HBMHBM3, then HBM2, and then HBMHBM, then HBM2, and then HBM3HBM, then HBM3, and then HBM2HBM2, then HBM, and then HBM3 Using the general decision rule for constrained capacity, what is the most Pearl should be willing to pay per hour for a worker to duplicate and pack DVDs after her normal working hours? (Assume that the worker would work at the same pace as Pearl.) (Round entry to 2 decimal places, e.g. 5.35.) Willing to pay: $ per hour

Answer 1

1) As the available hours is limited, constrained resource here is hours. To maximize firm's overall profit, constrained resource shall be utilized to satisfy the demand for the product that yields the highest contribution margin per hour fully first and then if balance is available, it must be used to satisfy demand for the next highest contribution margin per hour yielding product. Finally, if constrained resource is available after meeting demands for the highest contribution margin per hour yielding products, it must be utilized for the least contribution margin per hour yielding product. That is, Selling price Less: Variable costs-Blank DVD Less: Variable costs-Instructions and packaging Contribution margin per unit Number of units produced per hour Contribution margin per hour HBM HBM2 HBM3 $48.00 $28.30 $28.30 -$1.20 -$0.70 $0.70 -$3.80 -$1.80 $1.80 --> (B) $43.00 $25.80 $25.80 --> (A) - (B) 20 30 45 $860 $774 $1,161 --> HBM3 has the highest contribution margin per hour ($43 x 20) ($25.8 x 30) ($25.8 x 45) NOTE: As the prorated development costs is fixed in nature, it shall not be considered for calculating contribution margin.

2) HBM3 yields the highest, HBM yields the next highest and HBM2 yields the least contribution margin per hour. So, Product Order of Production 1 2 HBM3 HBM 3 HBM2 3) 2 Hours required to satisfy HBM3's daily demand Hours required to satisfy HBM's daily demand Total hours per day required to satisfy these two [90 games / 45 games per hour] [120 games / 20 games per hour] 6 8 As total hours available per day is utilized to produce first 2 products, firm needs balance hours to produce third product. 4 Hours required to satisfy HBM2's daily demand Contribution margin per hour Maximum pay can be offerred per day Number of hours per day (given) Maximum pay can be offerred per hour [120 games / 30 games per hour] [As calculated in Part-1] [4 hours x $774] $774 $3,096 8 $387.00 [$3096 / 8 hours)