The city of Metropolis is in the process of designing a new public emergency sys

Question

The city of Metropolis is in the process of designing a new public emergency system, and their design call for locating emergency vehicles around the city. The city is divided into nine districts, and seven potential sites have been identified as possible locations for emergency vehicles. Equipment located at each potential sire can reach some (but not all) of the districts within the 3-minutes time requirement specified by the city. In the following table, an entry of 1 means that the district can be serviced from the corresponding site within the time requirements. The city wants to provide coverage to all nine districts within the specified time, using the minimum number of sites.

Explanation / Answer

We need to find the minimum number of sites to cover all nine districts.

First , we need to select the Site, which can cover the maximum number of districts.

Number of districts covered by Site S1 = 5

Number of districts covered by Site S2 = 3

Number of districts covered by Site S3 = 3

Number of districts covered by Site S4 = 3

Number of districts covered by Site S5 = 4

Number of districts covered by Site S6 = 4

Number of districts covered by Site S7 = 4

Maximum number of districts covered is by Site 1. Site 1 covers the district

D2, D5, D6, D7, D9

So, first site is S1.

Removing these districts we get the districts

D1, D3, D4, D8

Now, we need to select the Site, which can cover the maximum number of remaining districts D1, D3, D4, D8

Number of districts covered by Site S2 = 3

Number of districts covered by Site S3 = 2

Number of districts covered by Site S4 = 2

Number of districts covered by Site S5 = 2

Number of districts covered by Site S6 = 2

Number of districts covered by Site S7 = 2

Maximum number of districts covered is by Site 2. Site 2 covers the district

D1, D3, D4

So, second site is S2.

Removing these districts we get the districts

D8

So, next site will be any site covering D8 which can be S3, S4 or S5.

So, Sites which can be used to cover all the districts are

(S1, S2 , S3)

or,

(S1, S2 , S4)

or,

(S1, S2 , S5)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.