[SOLVED] Develop a linear programming model

1. Develop a linear programming model Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD’s business involves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations.

 

Develop a linear programming model that can be used to find the minimum time required to make a delivery from location 1 to location 6. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

 

Min fill in the blank 1
x12 + fill in the blank 2
x13 + fill in the blank 3
x23 + fill in the blank 4
x24 + fill in the blank 5
x26 + fill in the blank 6
x32 + fill in the blank 7
x35 + fill in the blank 8
x42
+ fill in the blank 9
x45 + fill in the blank 10
x46 + fill in the blank 11
x53 + fill in the blank 12
x54 + fill in the blank 13
x56
s.t.

Flow Out Flow In
Node 1 fill in the blank 14
x12 + fill in the blank 15
x13 = fill in the blank 16
Node 2 fill in the blank 17
x23 + fill in the blank 18
x24 + fill in the blank 19
x26 +fill in the blank 20
x12 + fill in the blank 21
x32 + fill in the blank 22
x42 = fill in the blank 23
Node 3 fill in the blank 24
x32 + fill in the blank 25
x35 +fill in the blank 26
x13 + fill in the blank 27
x23 +fill in the blank 28
x53 = fill in the blank 29
Node 4 fill in the blank 30
x42 + fill in the blank 31
x45 + fill in the blank 32
x46 + fill in the blank 33
x24 + fill in the blank 34
x54 = fill in the blank 35
Node 5 fill in the blank 36
x53 + fill in the blank 37
x54 + fill in the blank 38
x56 + fill in the blank 39
x35 + fill in the blank 40
x45 = fill in the blank 41
Node 6 + fill in the blank 42
x26 + fill in the blank 43
x46 + fill in the blank 44
x56 = fill in the blank 45
xij ≥ 0 for all i, j

How long does it take to make a delivery from location 1 to location 6?

fill in the blank 46
minutes

Assume that it is now 1:00 P.M. and that CARD just received a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the guaranteed delivery time if the package picked up at location 1 is to be delivered to location 6?

fill in the blank 47
p.m.