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.
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Min fill in the blank 1×12 + fill in the blank 2×13 + fill in the blank 3×23 + fill in the blank 4×24 + fill in the blank 5×26 + fill in the blank 6×32 + fill in the blank 7×35 + fill in the blank 8×42+ fill in the blank 9×45 + fill in the blank 10×46 + fill in the blank 11×53 + fill in the blank 12×54 + fill in the blank 13x56s.t.
Flow Out Flow InNode 1 fill in the blank 14×12 + fill in the blank 15×13 = fill in the blank 16Node 2 fill in the blank 17×23 + fill in the blank 18×24 + fill in the blank 19×26 +fill in the blank 20×12 + fill in the blank 21×32 + fill in the blank 22×42 = fill in the blank 23Node 3 fill in the blank 24×32 + fill in the blank 25×35 +fill in the blank 26×13 + fill in the blank 27×23 +fill in the blank 28×53 = fill in the blank 29Node 4 fill in the blank 30×42 + fill in the blank 31×45 + fill in the blank 32×46 + fill in the blank 33×24 + fill in the blank 34×54 = fill in the blank 35Node 5 fill in the blank 36×53 + fill in the blank 37×54 + fill in the blank 38×56 + fill in the blank 39×35 + fill in the blank 40×45 = fill in the blank 41Node 6 + fill in the blank 42×26 + fill in the blank 43×46 + fill in the blank 44×56 = fill in the blank 45xij ≥ 0 for all i, j
How long does it take to make a delivery from location 1 to location 6?
fill in the blank 46minutes
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 47p.m.
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