Problem 1 The Burger Doodle restaurant chain uses a distribution center to prepa

Question

Problem 1 The Burger Doodle restaurant chain uses a distribution center to prepare the food ingredients it provides its individual restaurants. The company is attempting to determine the location for a new distribution center that will service five restaurants. The (x, y) coordinates of the five restaurants and the annual number of 40-foot trailer trucks transported to each restaurant are as follows 9 Restaurant Indianapolis Kokomo Lebanon Crawfordsville Lafayette 10 52 30 40 30 35 45 60 Annual truck shipments 85 110 75 60 100 Consider each trip of a truck from a new distribution center to a restaurant as a one-way trip (i.e., trucks do not come back to the distribution center)

Explanation / Answer

a) min

Z = =(ABS(A1-15)+ABS(B1-12)+ABS(A1-10)+ABS(B1-30)+ABS(A1-52)+ABS(B1-35)+ABS(A1-30)+ABS(B1-45)+ABS(A1-40)+ABS(B1-60))

solving using excel we get

nearest option

hence

(40,45) is correct

b) Z =85*(ABS(A1-15)+85*ABS(B1-12)+110*ABS(A1-10)+110*ABS(B1-30)+75*ABS(A1-52)+75*ABS(B1-35)+60*ABS(A1-30)+60*ABS(B1-45)+100*ABS(A1-40)+100*ABS(B1-60))

nearest option

(40,45) is correct

c)

Min Z =

=(85*SQRT((A1-15)^2 +(B1-12)^2) +110* SQRT((A1-10)^2 +(B1-30)^2)+75*SQRT((A1-52)^2 +(B1-35)^2)+60*SQRT((A1-30)^2 +(B1-45)^2)+100*SQRT((A1-40)^2 +(B1-60)^2)

solving we get

A1 = 29.025

B1 = 40.379

nearest option are

hence 30,50 is correct

29.99992405 34.99998989 130.0000861

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