The Our-Bags-Don The Our-Bags-Don\'t Break (OBDB) plastic bag company manufactur

Question

The Our-Bags-Don

The Our-Bags-Don't Break (OBDB) plastic bag company manufactures three plastic refuse bags for home use: a 20 gallon garbage bag, a 30-gallon garbage bag, and a 33-gallon leaf-and-grass bag. Using purchased plastic material, three operations are required to produce each end product: cutting, sealing, and packaging. The production time required to process each type of bag in every operation and the maximum production time available for each operation are shown (note that the production time figures in this table are per box of each type of bag). If OBDB's profit contribution is $0.10 for each box of 20-gallon bags produced, $0.15 for each box of 30-gallon bags, and $0.20 for each box of 33-gallon bags, Develop the LP formulation that would help you determine the optimal mix (Make sure to define all your decision variables). Develop a standard form for your LP formulation and make sure to define all the new variables. How would you calculate your slack variables? Show with at least one constraint in your model.

Explanation / Answer

LET X1 BE THE NO. OF

20 gallon garbage bag

LET X2 BE THE NO. OF

30 gallon garbage bag

LET X3 BE THE NO. OF

33 gallon garbage bag

MAX Z=0.1X1+0.15X2+0.2X3

2X1+3X2+3X3<=2

2X1+2X2+3X3<=3

3X1+4X2+5X3<=4

X1,X2,X3>=0

STANDARD FORM

Z=0.1X1+0.15X2+0.2X3+0S1+0S2+0S3

2X1+3X2+3X3+S1=2

2X1+2X2+3X3+S2=3

3X1+4X2+5X3+S3=4

WHERE S1,S2,S3 ARE THE SLACK VARIABLES

X1,X2,X3>=0

WE CAN CALCULATE EACH SLACK VARIABLE WHILE SOLVING IT GRAPHICALLY AND THEN SATISFYING ALL THE CONSTRAINTS

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