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.

1. 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
xij 0 for alli,j

2. How long does it take to make a delivery from location 1 to location 6? fill in the blank 46 minutes
3. 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.