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# sol2 - t BB t the ending month t balance at...

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AMS 341 Spring, 2011 Homework Set # 2 — Solution Notes #2, 3.8: Let x 9 J be the pounds of grade 9 oranges used in orange juice. Similarly, define x 9 B , x 6 J , x 6 B . max z = 0 . 45( x 9 J + x 6 J ) + 0 . 3( x 9 B + x 6 B ) x 9 J + x 9 B 100 , 000 x 6 J + x 6 B 120 , 000 (9 x 9 J + 6 x 6 J ) / ( x 9 J + x 6 J ) 8 (9 x 9 B + 6 x 6 B ) / ( x 9 B + x 6 B ) 7 x 9 J ,x 9 B ,x 6 J ,x 6 B 0 #4, 3.10: We can define: A 3 j ( A 4 j ): # product A produced by assembly line j in March (April)(j=1 or 2) B 3 j ( B 4 j ): # product B produced by assembly line j in March (April)(j=1 or 2) AI 3 ( AI 4 ): # product A in inventory at the end of March (April) BI 3 ( BI 4 ): # product B in inventory at the end of March (April) min z = 5 * (0 . 15( A 31 + A 41 ) + 0 . 12( B 31 + B 41 ) + 0 . 16( A 32 + A 42 ) + 0 . 14( B 32 + B 42 ))+ 0 . 2 * ( AI 3 + AI 4 + BI 3 + BI 4 ) s . t . 0 . 15 A 31 + 0 . 12 B 31 800 0 . 15 A 41 + 0 . 12 B 41 400 0 . 16 A 32 + 0 . 14 B 32 2000 0 . 16 A 42 + 0 . 14 B 42 1200 500 + A 31 + A 32 - AI 3 = 5000 750 + B 31 + B 32 - BI 3 = 2000 AI 3 + A 41 + A 42 - AI 4 = 8000 AI 3 + B 41 + B 42 - BI 4 = 4000 AI 4 1000 BI 4 1000 All variables 0 #8 3.11: Let BS t the ending balance at Saks in month
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Unformatted text preview: t , BB t the ending month t balance at Bloomingdale’s, and BM t the ending month t balance at Macy’s. PS t payment at month t to Sacks, PB t payment at month t to Bllomingdale’s, PM t payment at month t to Macy’s. min z = ∑ 36 t =1 ( PS t + PB t + PM t ) s . t . PB t + PS t + PM t ≤ 5000 t = 1 , 2 , ..., 36 BS = 20000 BB = 50000 BM = 40000 BS 36 = 0 BB 36 = 0 BM 36 = 0 BS t = BS t-1-( PS t-. 005 BS t-1 ) t = 1 , 2 , ..., 35 BB t = BB t-1-( PB t-. 01 BB t-1 ) t = 1 , 2 , ..., 35 BM t = BM t-1-( PM t-. 015 BM t-1 ) t = 1 , 2 , ..., 35 All variables ≥...
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