Due to Increased Sales, a Company Is Considering Building Three

Multiple Choice

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars) . The cost to operate DC 2 is $600 (in thousands of dollars.) . The cost to operate DC 3 is $525 (in thousands of dollars) . Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision.

The table below shows the cost ($ per item) for shipping from each DC to each region.
Region
$$\begin{array} { | c | c | c | c | c | } \hline \mathrm { DC } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \\\hline 1 & 1 & 3 & 3 & 2 \\\hline 2 & 2 & 4 & 1 & 3 \\\hline 3 & 3 & 2 & 2 & 3 \\\hline\end{array}$$ The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units.
Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4.
Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3.
-The constraint for distribution center 1 is:

A) X11 + X12 +X13 + X14 - 500y1 ? 0
B) X11 + X12 +X13 + X14D + 500y1 ? 0
C) X11 + X12 +X13 + X14 ? 500
D) X11 + X12 +X13 + X14 ? 500