✏️ 3/7 수업 필기

• 선형계획법

1. 결정 변수 : s (small chess set의 개수), l (large chess set의 개수)
2. 제약 : 3s + 2l <= 160, 1s+ 3l <= 200, s >= 0, l >= 0
3. 목적 함수 : max 5s + 20l
   --> optimal solution (0, 200/3)

p5.

• Simple upper and lower bounds

1. Sell4, <= 100 (upper bound)
2. Send6, boston >= 20 (lower bound)
3. Send5, paris == 30
4. -(무한대) <= eflow <= (무한대) -> 모형에서는 없어도 되는 제약식

p7.

• Flow constraints

1. Supply1 + Supply2 + Supply3 <= 1000
2. Buy1 + Buy2 + Buy3 >= 5000
3. 99/100buy1 + 98/100buy2 == (or >=) 100,000

p.9

• Simple resource constraints

1. 8makeI + 5makeH <= 10000
2. (시그마)(Costi * Acti) <= 150
3. c1 c2 사용가능
   (gram) 50 130 10000
   (kg) 1 1.5 200

50make1 130make2 <= 10000
make1 1.5make2 <= 200

p.11

• Material balance constraints
  L + flowin1 + flowin2 + flowin3 = flowout1 + flowout2 + flowout3

p.12

• Quality requirements
  ppt에 있는 걸로는 제약식이 부족해
  ex)
  food1 : fat 15%
  food2 : fat 2%
  food3 : fat 4%
  mixture: fat 5 ~ 10%

5/100 <= (0.15food1 + 0.02food2 + 0.04food3) / (food1 + food2 + food3) <= 10/100

==> 선형으로 바꾸기
0.05(food1 + food2 + food3) <= 0.15food1 + 0.02food2 + 0.04food3
0.15food1 + 0.02food2 + 0.04food3 <= 0.1(food1 + food2 + food3)

p.13

• Blending constraints
  raw1 : raw2 : raw3 = 6 : 3 : 1

raw1/(raw1 + raw2 + raw3) = 6/10
raw2/(raw1 + raw2 + raw3) = 3/10
raw3/(raw1 + raw2 + raw3) = 1/10

==> 선형제약식으로
10raw1 = 6(raw1 + raw2 + raw3)
10raw2 = 3(raw1 + raw2 + raw3)
10raw3 = (raw1 + raw2 + raw3)