Question

2) Consider the data provided below for three products Product Selling Unit direct Unit Unit Unit Unit price material direct outsourcing overhead processing labor cost (S) time at the bottleneck (hrs 125 250 200 25 100 110 35 35 35 25 25 25 12 2.5 12 There is 600 total available machine-hours on the bottleneck machine. The sales department estimates the maximum sales for each product to be as follows: A : maximum 70 B:maximum 120 C:maximum 220 a) What is the unit profit of each product in the sense of classical cost accounting? Show work. b) What is the contribution margin of each product in the TOC sense? Show work c) What is the best product mix that will maximize the throughput (in the TOC sense)? Show work. d) Write down the corresponding LP problem, when solved will give the optimal product mix

Answer 1

a) classical cost accountng roduct schedule Selling price 1 125 250 200 unit direct material cost unit direct labor cost unit outsourcing cost unit overhead cost total cost 25 35 25 12 97 28 100 35 25 12 172 78 110 35 25 12 182 18 Unit profit (selling price total cost) b) contribution margin per hour of processing time unit processing time at the bottleneck (hrs) i.e. time of constraint 2.5 throughput (contributions margin) 5 (1-2) 100 150 90 throughput per hour of processing (in $) 6 5/4 100 60 45 production priority c) as per production priority in answer b maximum sale capacity 70 best product mix machine hours consumed machine hour product working Note required per unit 70produce maximum sale capacity can produce maximum sale capacity as 120 2.5 120 300 achine hours remaining can fullfill remaining machine hours are (600 70 | 300) i.e. 230 hours produce possible quantity of C. 220 115 230 600 d) corresponding linear programming problem maximize profit Z 28 78 b 18c whether a-sale units of product A, b-sale units of product B , C Subject to following conditions, a +2.5 b2C< 600, a < 70 , b <: 120 , c <-220 and a 0, b> 0, c> 0, sale units of product C this condition is for the machine hours available