LEGEND  Xij = # of 1000 lb. loads from International port i…

LEGEND  Xij = # of 1000 lb. loads from International port i to US port j.   i=1=Tokyo;    j=4=Norfolk;      k=6=Houston                   Wjk = # of 1000 lb. loads from US port j to US DC k.                    2=Manilla;      5=Savanna;         7=Detroit                   Uik = # of 1000 lb. loads from International port i to US DC k.     3=Beijing;                                   8=Dayton      MIN 420X14+610X15+510X24+470X25+450X34+400X35+390U38+75W46+90W47+81W48+68W56+82W57+95W58  S.T.1)  1X14 + 1X15 ≤ 95                                                                 Supply limit at Tokyo port (1000 lb loads)        2)  1X24 + 1X25 ≤ 60                                                                 Supply limit at Manilla port (1000 lb loads)        3)  1X34 + 1X35 + 1U38 ≤ 85                                                    Supply limit at Beijing port (1000 lb loads)        4)  1X14 + 1X24 + 1X34 – 1W46 – 1W47 – 1W48 = 0            Flow balance at Norfolk port (1000 lb loads)        5)  1X15 + 1X25 + 1X35 – 1W56 – 1W57 – 1W58 = 0            Flow balance at Savannah port (1000 lb loads)        6)  1W46 + 1W56 = 75                                                               Demand at Houston distribution center (1000 lb loads)        7)  1W47 + 1W57 = 80                                                               Demand at Detroit distribution center (1000 lb loads)        8)  1U38 + 1W48 + 1W58 = 65                                                  Demand at Dayton distribution center (1000 lb loads)        9)  1X25 ≤ 50                                                                              Manila to Savannah limit (1000 lb loads)       10)  1W48 ≥ 30                                                                            Norfolk to Dayton minimum (1000 lb loads)       11)  Xij ≥ 0 for all i,j                                                                    Non-negativity       12)  Wjk ≥ 0 for all j,k                                                                  Non-negativity       13)  Uik ≥ 0 for all i,k                                                                   Non-negativity    Using the Polymers Inc, how much should be shipped on the route from Tokyo to Norfolk?

Silver Star Company Legend Xij = number of product i from s…

Silver Star Company Legend Xij = number of product i from source j, where i = 1 small 12 oz., 2 medium 16 oz., or 3 large 24 oz.                                                                             j = 1 Plant 1, 2 Plant 2, 3 Plant 3, 4 Supplier Zj = 1 if source j is setup, 0 otherwise; where j = 1 Plant 1, 2 Plant 2, 3 Plant 3, 4 Supplier   MAX 9X11+11X21+15X31+11X12+12X22+16X32+10X13+13X23+17X33+8X14+10X24+12X34-20000Z1 -30000Z2-25000Z3-2000Z4   S.T. 1)  3X11 + 4X21 + 5X31 – 80000Z1 ≤ 0        Plant 1 capacity (min); Plant 1 setup if used 2)  6X12 + 7X22 + 8X32 – 90000Z2 ≤ 0        Plant 2 capacity (min); Plant 2 setup if used 3)  6X13 + 5X23 + 4X33 – 80000Z3 ≤ 0        Plant 3 capacity (min); Plant 3 setup if used 4)  1X14 + 1X24 + 1X34 – 40000Z4 ≤ 0        Supplier capacity (bottles); Supplier setup if used 5)  1X11 + 1X12 + 1X13 + 1X14 = 18000      Demand for product 1 small 12 oz. bottles 6)  1X21 + 1X22 + 1X23 + 1X24 = 10000      Demand for product 2 medium 16 oz. bottles 7)  1X31 + 1X32 + 1X33 + 1X34 = 12000      Demand for product 3 large 24 oz. bottles 8)  Xij ≥ 0 for all i,j                                          Non-negativity 9)  Zj =1 or 0 for all j                                       Binary constraints Using the Silver Star output, which of the following constraints will meet demand despite medium 16 oz. bottle yields of only 95% at each of the plants 1, 2, and 3, as well as at the supplier?