Blog

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?