# (Solved Homework): Four hospitals located within a city are cooperating to establish a centralized blood-bank…

Four hospitals located within a city are cooperating to establish a centralized blood-bank facility that will serve the hospitals. The new facility is to be located such that distance traveled is minimized. The hospitals are located as follows: P_1 = (5, 10), P_2 = (7, 6), P_3 = (4, 2), and P_4 = (16, 3). The number of deliveries to be made per year between the blood-bank facility and each hospital is estimated to be 450, 1200, 300, and 1500, respectively. Assuming rectilinear travel, determine the optimum location. What assumption must be made concerning the deliveries of blood? Is it reasonable to expect delivery trips will always be to only one hospital when a delivery is made?

Using center of gravity method, we can determine optimal point or location from where the blood bank can service the four hospitals.

First we determine the x-coordinate of the center of gravity by taking all x axis numbers for the given four Hospital locations and multiply them with the weight of deliveries per year.

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We get

x coordinate for center of gravity = [5(450) + 7(1200) + 4(300) + 16(1500)] / [450+ 1200 + 300 + 1500] = 10.39

Now, we calculate the center of gravity for y-axis using same process as above

We get

y coordinate for center of gravity = [10(450) + 6(1200) + 2(300) + 3(1500)] / [450+ 1200 + 300 + 1500] = 4.87

Taking the x and y coordinated calculated above for the center of gravity, we get

optimal location point to be (10.39, 4.87)

Since we have calculated on the basis of rectilinear or straight line distances for the deliveries from blood bank to hospitals, we also assume that there would be one delivery to one hospital per trip.

We cannot expect in the normal situation that the trips will be one-to-one, since delivery requests for may come from different hospitals at the same time. The optimum delivery point can be recalculated, if we know the frequency of deliveries, capacity of transport vehicle, costs and other variables.

In the absence of these other information, we can reasonably estimate the central location to be as calculated above on the assumption that one delivery ISI made to one hospital at a time.

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