Midterm Review AOS

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University of Pittsburgh *

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1090

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Electrical Engineering

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Dec 6, 2023

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#aos#prep23 10 questions on midterm
The Rappaport Communications Company provides cellular telephone services in several mid-western states. The company is planning to expand its customer base by offering cellular service in northeastern Ohio to the cities of Cleveland, Akron, Canton, and Youngstown. The company will install the hardware necessary to service customers in each city on pre existing communications towers in each city. The locations of these towers are summarized below: The company also needs to construct a new communications tower some-where between these cities to handle intercity calls/ This tower will also allow cellular calls to be routed onto the satellite system for worldwide calling service. The tower the company is planning to build can cover areas within a 40-mile radius. Thus, the tower needs to be located within 40 miles of each of these cities. Where should we build the communications tower to minimize the sum of the distances to the given cities? Formulate the problem Tower location -> x,y cord Constr. Within 40 miles from each city Obj. min sum of distance , Tower C1, C2, C3 D.V x,y -> coordinates of tower Assume Cleveland -> xc, yc Akron -> xa, ya Canton -> xca, yca youngstown , xy, yy Obj. min distance
Min [sqrt ((x-xc) ^2 + (y-yc)^2) sqrt ((x-xa) ^2 + (y-ya)^2) sqrt ((x-xca) ^2 + (y-yca)^2) sqrt ((x-xy) ^2 + (y-yy)^2)] Constraint: [sqrt ((x-xc) ^2 + (y-yc)^2) sqrt ((x-xa) ^2 + (y-ya)^2) sqrt ((x-xca) ^2 + (y-yca)^2) sqrt ((x-xy) ^2 + (y-yy)^2)] <= 40
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