Question

Questions 22-24 rely on the following prompt:

Two street vendors (Vendor 1 and Vendor 2) with mobile carts produce the same good which they sell at the same price. Customers are located along a linear boardwalk with six locations (Location A through Location F), with a different number of customers in each location, as pictured below:

18 So, there are X customers in location A, 4 in B, 6 in C, 2 in D, 8 in E and 18 in F. There are 38+ X customers total. Customers will make a purchase from whichever vendor is closest to them, and equally close customers will be split evenly between Vendor 1 and Vendor 2. The vendors CAN locate in the same location (so, both could locate in location A) 22. If X- 12, where will Vendor 1 locate in equilibrium? a. A b. B d. D 23. If X = 12, where will Vendor 2 locate in equilibrium? a. A b. B d. D 24. What is the smallest value of X that would make (A, A) an equilibrium?

Answer 1

22.The total number of customers = X+38

If X=12 then total number of customers = 12+38=50 and total number of locations =6

and equilibrium number of customers = 50/6=8.33 which is nearest value to number of customers i.e., 8 in point E.

Therefore, the vendor 1 will relocate to location E.

The correct answer is e) E

23. The equilibrium location is E when X =12 from part 22. Therefore, vendor 2 will also relocate to location E as in this case, both vendors can move into same location.

The correct answer is e. E

24 if X=7

then equilibrium value of customers = (38+7)/6=7.5 which is nearest to 7.

Again if X=5, then

equilibrium value of customers = (38+5)/6= 7.16 which is also nearest to 7.

Therefore, the smallest value of X is 7 that will make (A,A) an equilibrium.