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Business Management Assignment

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Submitted By jaeyong
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2장 연습문제 B
>문제
1.K스포츠기구사는 일반 야구글러브와 캐쳐용 야구글러브를 생산한다. 글러브는 봉제공정, 마무리공정, 포장 및 수송공정을 거쳐서 생산되는데 이 회사에서 다음달에 동원할 수 있는 생산능력은 봉제공정이 900시간, 마무리공정이 300시간, 그리고 포장/수송공정이 100시간이다. 각 제품생산에 투입되는 각 공정의 생산시간과 새당 이익은 다음표와 같다. 제품 | 봉제공정 | 마무리공정 | 포장수송 | 개당이익 | 일반글러브 | 1시간 | 1/2시간 | 1/8시간 | 25,000원 | 캐쳐용 글러브 | 3/2시간 | 1/3시간 | 1/4시간 | 40,000원 |
총 이익을 최대화 할 수 있는 선형계획모형을 개발하시오.

>풀이
X1 = 일반글러브 개수, X2 = 캐쳐용 글러브 개수
Max Z = 25000X1+40000X2
ST. X1+3/2X2=<900(봉제공정) 1/2X1+1/3X2=<300(마무리공정) 1/8X1+1/4X2=<100(포장수송공정) X1, X2>=0(비음제약식)
최적해 (X1,X2) =(500,150)
최대이익 : 18,500,000원

>문제
2. 소와 염소를 기르는 농장에서는 보레토와 칼파를 섞어서 사료로 쓰고 있다. 보레토 한 부대는 10,000원이고 100단위의 칼슘과 400단위의 단백질을 갖고 있고, 칼파 한 부대는 15,000원이고200단위의 칼슘과 200단위의 단백질을 갖고 있다. 이 농장에 있는 가축들을 하루 먹이는 데에는 6,000단위의 칼슘과 12,000단위의 단백질이 소요된다. 또한 사료공급업자와의 계약조건에 따르면 칼파 한 부대를 사기 위해서는 보레토를 최소한 2부대를 사야만 한다. 총 비용을 최소화 할 수 있는 선형계획모형을 개발하시오.

>풀이 제품 | 칼슘 | 단백질 | 가격 | 보레토(X1) | 100 | 400 | 10,000 | 칼파(X2) | 200 | 200 | 15,000 |
X1 = 보레토의 개수, X2 = 칼파의 개수
Min = 10,000X1+15,000X2
ST. 100X1+200X2>=6,000(칼슘) 400X1+200X2>=12000(단백질) 2X1>=X2(칼파1부대는 최소한 보레토2부대) X1,X2>=0(비음제약식)

최적해(X1, X2) =(20,20)
최소 비용 : 500,000

>문제
3. L전자에서는 계산기용 IC칩을 생산하고 있다. L전자는 두 개의 공장을 통하여 IC칩을 생산하며 5개의 도매상에게 판매하고 있다. 공장 1과 공장 2에서의 개당 생산비용은 21,900원, 23,800원이다. 수요예측에 의하면 도매상 1,2,3,4,5에게 각각 2,000개, 3,000개 1,000개, 5,000개, 4,000개를 공급해야 한다. 한 개의 IC칩을 한 공장에서 도매상에게 넘기는 데 드는 수송비 및 취급비용은 아래의 표와 같다. (단위 : 원/개) | 1 | 2 | 3 | 4 | 5 | 1 | 300 | 200 | 500 | 400 | 200 | 2 | 600 | 400 | 200 | 300 | 500 |
각 공장에서의 생산능력은 각각8,000개이다. 각 공장에서의 생산량 및 수송계획을 최적으로 구할 수 있는 선형계획모형을 개발하시오.

>풀이
Xij = i공장에서 생산해서 j공장으로 보내는 IC칩의 개수
Min Z = 22,200X11+22,100X12+22,400X13+22,300X14+22,100X15 +24,400X21+24,200X22+24,000X23+24,100X24+24,300X25
ST.

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