Problem 2 Storex manufactures three types of computer storage disk packs: M1, M2 and M3. Each disk pack must go through four different production phases: cutting, cleaning, and coating, testing and assembly. We have the following set of information with which to make a product mix decision for the company: Processing hours Mi M2 M Total hours available per week 0.2 0.8 1.2 23 2.4 5 3200 8000 Cutting Cleaning and coating Testing Assembly Profit margin 0.8 0.2 0.3 50 12 2 320 2400 4800 1 150 Let x1, x2 and x3, respectively, be the quantities of M2 M2, and Ma to be produced, and let s, 52, 53 and se respectively, be the slack variables representing the unused hours of the cutting, cleaning and coating. testing and assembly facilities. The simplex tableau for an optimum solution of the problem is given below: X: 0 1 0 0 0 SE 0 0 X 0 0 1 0 0 X 1 0 0 0 0 S2 0,34 2,06 -1.03 -0,27 Si 0,77 -5,34 0,17 -0,12 6.89 S; -2.15 2.06 3,96 -0,27 8,62 0 1 0 68,97 4413,79 1793,10 1544,83 511,72 58,62 1. What are the shadow prices of the four production processes? What do these shadow prices mean? 2. A competitor has just introduced a new disk pack. Each unit of this disk pack will require 3 hours of cutting, 5 hours of cleaning and coating, 3 hours of testing, and 4 hours of assembly. The profit margin on this new disk pack will be 350. Should Storex bring out the new type of disk pack? Problem 2 Storex manufactures three types of computer storage disk packs: M1, M2 and M3. Each disk pack must go through four different production phases: cutting, cleaning, and coating, testing and assembly. We have the following set of information with which to make a product mix decision for the company: Processing hours Mi M2 M Total hours available per week 0.2 0.8 1.2 23 2.4 5 3200 8000 Cutting Cleaning and coating Testing Assembly Profit margin 0.8 0.2 0.3 50 12 2 320 2400 4800 1 150 Let x1, x2 and x3, respectively, be the quantities of M2 M2, and Ma to be produced, and let s, 52, 53 and se respectively, be the slack variables representing the unused hours of the cutting, cleaning and coating. testing and assembly facilities. The simplex tableau for an optimum solution of the problem is given below: X: 0 1 0 0 0 SE 0 0 X 0 0 1 0 0 X 1 0 0 0 0 S2 0,34 2,06 -1.03 -0,27 Si 0,77 -5,34 0,17 -0,12 6.89 S; -2.15 2.06 3,96 -0,27 8,62 0 1 0 68,97 4413,79 1793,10 1544,83 511,72 58,62 1. What are the shadow prices of the four production processes? What do these shadow prices mean? 2. A competitor has just introduced a new disk pack. Each unit of this disk pack will require 3 hours of cutting, 5 hours of cleaning and coating, 3 hours of testing, and 4 hours of assembly. The profit margin on this new disk pack will be 350. Should Storex bring out the new type of disk pack
