Textile Mill

Assuming, X1 = Yards of Fabric 1 Purchased X12 = Yards of Fabric 1 on Dobbie Looms X2 = Yards of Fabric 2 Purchased X21 = Yards of Fabric 2 on Dobbie Looms X3 = Yards of Fabric 3 Purchased X31 = Yards of Fabric 3 on Dobbie Looms X32 = Yards of Fabric 3 on Regular Looms X4 = Yards of Fabric 4 Purchased X41 = Yards of Fabric 4 on Dobbie Looms X42 = Yards of Fabric 4 on Regular Looms X5 = Yards of Fabric 5 Purchased X51 = Yards of Fabric 5 on Dobbie Looms X52 = Yards of Fabric 5 on Regular Looms

Production Times in Hours per Yard:
Fabric | Dobbie | Regular |
1 | 1 / 4.63 = 0.215983 | - |
2 | 1 / 4.63 = 0.215983 | - |
3 | 1 / 5.23 = 0.191205 | 1 / 5.23 = 0.191205 |
4 | 1 / 5.23 = 0.191205 | 1 / 5.23 = 0.191205 |
5 | 1 / 4.17 = 0.239808 | 1 / 4.17 = 0.239808 |

Profit Contribution per Yard:
Fabric | Manufactured (Variable cost –Selling Price) | Purchased (Selling Price – Purchase Price) |
1 | 0.99-0.66=0.33 | 0.99-0.80=0.19 |
2 | 0.86-0.55=0.31 | 0.86-0.70=0.16 |
3 | 1.10-0.49=0.61 | 1.10-0.60=0.50 |
4 | 1.24-0.51=0.73 | 1.24-0.70=0.54 |
5 | 0.70-.50=0.20 | 0.70-.70=0 |

Max Profit objective function
Max -
P = .19X1 + 0.33X12 + 0.16X2 + 0.31X21 + 0.5X3 + 0.16X31 + 0.16X32 + 0.54X4 + 0.73X41 + 0.73X42 + 0X5 + 0.2X51 + 0.2X52

Dobbie Hours Available: 8 Looms x 30 days x 24 hours/day = 5760
Regular Hours Available: 30 Looms x 30 days x 24 hours/day = 21600

Demand Constraints:
Constraint1: X1 + X12 = 16500
Constraint2: X2 + X21 = 22000
Constraint3: X3 + X31 + Y32 = 62000
Constraint4: X4 + X41 + X42 = 7500
Constraint5: X5 + X51 + X52 = 62000

Loom Constraints:
Constraint6: Dobbie Looms: 0.21598X12 + 0.21598X21 + 0.1912X31 + 0.1912X41 + 0.2398X51 ≤ 5760
Constraint7: Regular Looms: 0.192X32 + 0.1912X42 + 0.2398X52 ≤ 21600