Assignment#1:

Question#1:
The objective of our study is to maximize the profit that Maxwell Manufacturing makes by producing pens. | | Resources | | Profit | Decision Variable | Plastic | Ink assembly | Modeli. time | | Fliptop Model(X) | 3 | 5 | 5 | 1,000 | Tiptop Model(Y) | 4 | 4 | 2 | 1,000 | Total | 36 | 40 | 30 | |

Linear Model:
Maximize= 1,000 X+ 1,000 Y
S.T. 3X + 4Y ≤ 36 5X + 4Y ≤ 40 5X + 2Y ≤ 30 X, Y ≥ 0
Solution:
3X +4Y =36
5X + 4Y= 40
5X + 2Y= 30

Constraint 1 | Constraint 2 | Constraint 3 | 3X +4Y=36 | 5X + 4Y= 40 | 5X +2Y= 30 | IF X= 0 | IF X=0 | IF X=0 | Y=9 | Y=10 | Y=15 | IF Y=0 | IF Y=0 | IF Y=0 | X=12 | X=8 | X=6 |

Corners:
A→6, 0
B→3.2, 6.7
C→0, 10
Optimal solution:
Z= 1,000X + 1,000Y
A: 1,000(6) + 1,000 (0) = 6,000$
B: 1,000(3.2) + 1,000 (6.7) =9,900$
C: 1,000(0) + 1,000 (10) = 10,000$
Optimal Combination:
0 Fliptop Model
10 Tiptop Model

Question#2: | | Resources | | Profit | Decision Variable | Synthetic | Hours | Foam | | Grade X | 50 | 25 | 20 | 200 | Grade Y | 40 | 28 | 15 | 160 | Total | 3,000 | 1,800 | 1,500 | |

Linear Model:
Maximize = 200X + 160Y
S.T. 50X + 40Y ≤ 3,000 25X + 28Y ≤ 1,800 20X + 15Y ≤ 1,500 X, Y ≥0
Solution:
50x + 40y=3,000 25X + 28Y = 1,800 20X + 15Y = 1,500 Constraint 1 | Constraint 2 | Constraint 3 | 50X +40Y=3,000 | 25X + 28Y= 1,800 | 20X +15Y= 1,500 | IF X= 0 | IF X=0 | IF X=0 | Y=75 | Y=64.2 | Y=100 | IF Y=0 | IF Y=0 | IF Y=0 | X=60 | X=72 | X=75 |

Corners:
A→60, 0
B→32, 37
C→0, 65
Optimal solution:
Z= 200X + 160Y
A: 200(60) + 160 (0) = 12,000$
B: 200(32) + 160(37) =12,320$
C: 200(0) + 160 (10) = 10,400$
Optimal Combination:
32 Grade X
37 Grade