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 x 12 fill in the blank 2 x 13 fill in the blank 3 x 23 fill in the blank 4 x 24 fill in the blank 5 x 26 fill in the blank 6 x 32 fill in the blank 7 x 35 fill in the blank 8 x 42 fill in the blank 9 x 45 fill in the blank 10 x 46 fill in the blank 11 x 53 fill in the blank 12 x 54 fill in the blank 13 x 56 s t Flow Out Flow In Node 1 fill in the blank 14 x 12 fill in the blank 15 x 13 fill in the blank 16 Node 2 fill in the blank 17 x 23 fill in the blank 18 x 24 fill in the blank 19 x 26 fill in the blank 20 x 12 fill in the blank 21 x 32 fill in the blank 22 x 42 fill in the blank 23 Node 3 fill in the blank 24 x 32 fill in the blank 25 x 35 fill in the blank 26 x 13 fill in the blank 27 x 23 fill in the blank 28 x 53 fill in the blank 29 Node 4 fill in the blank 30 x 42 fill in the blank 31 x 45 fill in the blank 32 x 46 fill in the blank 33 x 24 fill in the blank 34 x 54 fill in the blank 35 Node 5 fill in the blank 36 x 53 fill in the blank 37 x 54 fill in the blank 38 x 56 fill in the blank 39 x 35 fill in the blank 40 x 45 fill in the blank 41 Node 6 fill in the blank 42 x 26 fill in the blank 43 x 46 fill in the blank 44 x 56 fill in the blank 45 x ij 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

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jul 06, 2024

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

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

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