A plumber can buy plastic pipe in 6-foot and 12-foot lengths. The current job re

Question

A plumber can buy plastic pipe in 6-foot and 12-foot lengths. The current job requires eight 4-foot lengths, five 5-foot lengths and three 7-foot lengths. The plumber wants to figure out how many of each of the two stock lengths should be bought to minimize waste. (e) Set up a linear programming model to the above situation. (0 Solve the model. (g) Perform a sensitivity analysis on the model. (h) Comment on the solution, noting the meanings of the slack variables and the ranges for resource and cost components.

Explanation / Answer

REQUIRED SIZES OF PIPES ARE `8` PIECES OF 4,FEET LENGTH

`5` PIECES OF 5, FEET LENGTH

AND `3` PIECES OF 7 FEET LENGTH AND AVAILABLE SIZE OF STOCK LENGTH 6 FEET AND 12 FEET.

TO MINIMIZE WASTE IT SHOULD BE SELECTED SUCH THAT CUTTING WASTAGE MINIMUM.

CLEARLY IF THREE PIECES OF 5 FEET AND THREE PIECES OF 7 FEET CAN BE CUT USING THREE

12 FEET STOCK LENGTH NO WASTAGE.

NOW REQUIRED LENGTH OF PIECES TWO 5 FEET AND 8 FOUR FEET PIECES.

AGAIN FROM 12 FEET STOCK LENGTH 6 FOUR FEET PIECES CAN BE CUT WITHOUT WASTAGE

TAKING TWO 12 FEET STOCK LENGTH.

HENCE TOTAL 12 FEET STOCK LENGTH REQUIRED ( 3+ 2) = 5

NOW TWO 4 FEET PIECES AND TWO 5 FEET PIECES REQUIRED FOR THIS TWO OPTIONS

IF TWO 5 FEET PICES ARE CUT FROM 12 FEET STOCK LENGTH WASTAGE = 2 FEET

AND TWO 4 FEET PIECES ARE CUT FROM 12 FEET STOCK LENGTH WASTAGE = 4 FEET

I.E TOTAL WASTAGE (2 + 4 ) = 6 FEET

IF TWO 5 FEET PIECES ARE CUT FROM TWO 6 FEET STOCK LENGTH WASTAGE = (1 + 1) FEET= 2 FEET

AND TWO 4 FEET PIECES CUT FROM 6 FEET STOCK LENGTH WASTAGE (2+2) FEET= 4 FEET

HENCE TOTAL WASTAGE (2 +4 ) FEET = 6 FEET ,BOTH CONDITION SAME WASTAGE

HENCE MOST SUITABLE OPTION ( 3 + 2 + 1 +1) =7 ,12 FEET STOCK LENGTH WITH WASTAGE 6 FEET

OR ( 3 +2 ) = 5 , 12 FEET STOCK LENGTH AND 4 , 6 FEET STOCK LENGTH

SLACK VARIABLES ARE THOSE VARIABLES WHICH ARE ADDED TO MAKE AN EQUALITY IN EQUATION

WHICH GIVES NO PROFIT.

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