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Due to Increased Sales, a Company Is Considering Building Three

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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
DCABCD113322241333223\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.
-You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.
Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, write the constraint(s) for the second restriction.

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Definitions:

Sympathetic Stimulation

Activation of the sympathetic nervous system, resulting in physiological responses such as increased heart rate and blood flow to muscles.

Metabolic Rate

The rate at which the body uses energy to maintain basic vital functions such as breathing, circulation, and cell production.

Precapillary Sphincters

Ring-like muscles located at the entrance of capillaries, controlling blood flow into the capillaries by contraction and relaxation.

Interstitial Pressure

The pressure within the space between cells, which can influence fluid movement and absorption in tissues.

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