The bookstore has decided to promote its new opening by having a shopping spree. The winner of the shopping spree will have to abide by the following rules. They will have 10 minutes to grab as many items as possible from the store. They must place a shopping cart in one spot and leave it there for the entire duration of the spree. Also they can only pick up one item at a time from the shelves and bring it to the cart. The following table provides a list of all of the items in the store (22), the X,Y coordinates of each item, the cost of each item, and the quantity available. It is estimated that a person can travel 20 feet in one second, therefore if an item is 100 feet away it will take a person 5 seconds to retrieve the item and 5 seconds to return it to a cart for a total of 10 seconds. The shopping cart must be placed inside of the store.
Product X Coordinate Y-Coordinate # Available $Cost
A 78 75 14 33
B 97 1 97 22
C 56 96 21 49
D 62 10 56 52
E 22 31 58 34
F 66 98 42 56
G 93 45 29 57
H 88 98 50 46
I 25 44 50 23
J 34 90 62 48
K 10 4 77 43
L 52 31 3 58
M 44 35 36 40
N 66 16 14 37
O 3 50 23 22
P 99 61 75 35
Q 79 16 16 48
R 13 62 13 37
S 5 84 4 28
T 9 80 23 118
U 20 67 82 24
V 95 84 8 56
A. Assuming the shopping cart must be placed at X,Y coordinates (0,0) and assuming Euclidean distances, what is the maximum profit a contestant can achieve from the shopping spree? (Remember, maximum profit for the contestant is maximum loss for the book store.)
B. Assuming the shopping cart must be placed at X,Y coordinates (0,0) and assuming Rectilinear (right angle) distances, what is the maximum profit a contestant can achieve from the shopping spree? (Remember, maximum profit for the contestant is maximum loss for the book store.)
C. Assuming you can place the shopping cart anywhere and assuming Euclidean distances, what is the maximum profit a contestant can achieve from the shopping spree? Also, where should the contestant place the shopping cart in order to maximize their profit? Provide the solution that Open Office solver gives and provide a model or logic of your formulation. (Remember, maximum profit for the contestant is maximum loss for the book store.)
D. Assuming you can place the shopping cart anywhere and assuming Rectilinear distances (right angle), what is the maximum profit a contestant can achieve from the shopping spree? Also, where should the contestant place the shopping cart in order to maximize their profit? Provide the solution that Open Office solver gives and provide a model or logic of your formulation. (Remember, maximum profit for the contestant is maximum loss for the book store.)