a) Decision variables:
Xi=quantity produced in month I on a regular time basis for i=1234 Yi= quantity produced in month I on overtime for i=1234 Zi= quantity in inventory at the end of month i for i=1234 Where i=1234 month January to April Objective function and the constraints:
Minimize Z=500(X1+X2+X3+X4)+650(Y1+Y2+Y3+Y4)+40(Z1+Z2+Z3+Z4)
Subject to:
Regular time production constraint for each month X1<=3000 X2<=2000 X3<=3000 X4<=3500 Overtime production constraint for each month Y1<=500 Y2<=400 Y3<=600 Y4<=800 The beginning inventory + total production minus = the demand for particular month.
X1+Y1-Z1=2800
Z1+X2+Y2-Z2=3000
Z2+X3+Y3-Z3=3500
Z3+X4+Y4-Z4=3000
The inventory constraints can be formulated as follows:
Z1>=100
Z2>=100
Z3>=100
Z4>=300
All Xi, Yi, Zi>=0 for i=1, 2, 3, 4 b) X1=3000 Quantity produced in January on a regular time basis X2=2000 Quantity produced in February on a regular time basis X3=3000 Quantity produced in March on a regular time basis X4=3200 Quantity produced in April on a regular time basis Y1=500 Quantity produced in January on overtime Y2=400 Quantity produced in February on overtime Y3=500 Quantity produced in March on overtime Z1=700 Quantity produced in inventory at the end of January Z2=100 Quantity produced in inventory at the end of February Z3=100 Quantity produced in inventory at the end of March Z4=300 Quantity produced in inventory at the end of April Z=$6, 558, 000. 00 Question3 a) Let X1 = a number of 8-foot and 10-foot cuts X2 = a number of 8-foot and 12-foot cuts X3 = a number of two 8-foot cuts X4 = a number of two 10-foot cuts The LP model is, Minimize Z= 2X1+0X2+4X3+0X4=2X1+4X3 Subject toX1+X2+X3+X4 350 X1+X2+2X3 276 X1+2X4 100 X2 250 X1, X2, X3, and X4 0 b) i) The amount of waste that wo...
