Question

The Mead Paper Company produces rolls of paper for cash registers and office equipment. The rolls are cut in widths of 2, 3 and 4 inches. Before cutting, the rolls arrive 10 inches wide. The company must decide how to produce the three different widths efficiently without wasting any paper. The following table shows five cutting alternatives to consider. Number Rolls of Cut alternative 2 in 3 in 4in 0 0 3 0 2 2 0 0 4 0 The minimum requirements for the three products are 1200 units of 2 inch rolls, 1800 units of 3 inch rolls, and 1000 units of 4 inch rolls. If the company wants to minimize the number of 10 inch rolls that must be cut, how many 10 inch rolls will need to be processed on each cutting alternatives? Create the entire linear programming model below and plug into LINDO and interpret AND show the results. (Hint: Let Xi- number of 10 inch rolls of paper processed by cutting alternative i, where i-1,2,3,4,5.)

Answer 1

Solution:

Linear Programming model is as follows

Let Xi = number of 10 inch rolls of paper processed by cutting alternative i, where i ϵ {1,2,3,4,5}

Min X1+X2+X3+X4+X5

s.t.

5X1+0X2+2X3+1X4+3X5 >= 1200

0X1+3X2+2X3+1X4+0X5 >= 1800

0X1+0X2+0X3+1X4+1X5 >= 1000

Xi >= 0

Solution using LINDO is as follows:

Solution:

X1 = 0

X2 = 200

X3 = 100

X4 = 1000

X5 = 0

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