Question

Exxon Corporation has two refineries where JP-8 fuel is produced. The refineries are located in (A) Nebraska and (B) Virginia. Refinery (A) has the capacity to produce 3500 barrels per month, while refinery (B) has the capacity to produce 5000 barrels per month. Exxon has an exclusive contract with the US Air Force to provide and ship all JP-8 fuel produced at these two refineries to USAF fuel depots located in (1) Tennessee, (2) Georgia, (3) North Carolina, (4) South Carolina, (5) Colorado, and (6) Utah. The Air Force assumes that monthly demand at each depot is known and does not change from one month to another. Monthly Demand at the depots 1, 2, 3, 4, 5, 6 is as follows: (1) 1500 barrels, (2) 1700 barrels, (3) 1400 barrels, (4) 950 barrels, (5) 1150 barrels, and (6) 1300 barrels. The cost to ship one barrel from the refineries (A or B) to the depots is provided in the following table:

Cost per Barrel to Ship To
Refinery	From/To	1	2	3	4	5	6
	A	$1.50	$1.35	$1.60	$1.45	$1.80	$1.75
	B	$1.25	$1.65	$1.40	$1.55	$1.20	$1.65

1. Formulate a linear program model to minimize total monthly shipping costs. Make the following additional assumptions:

1. Refineries have capacity to store undistributed fuel.
2. Demand must be met with Exxon-produced JP-8 fuel.

All You need is:

Decision Variable

Objective Function

Constraints

Answer 1

OBJECTIVE; To formulate a linear programming rodes to minimize total monthly Shipping costs. Assumptions: o refineries undistributed ② demand must be have capacity to store fuel. Exxm - produced JP-8 full, met with Given. Refineries Capacity (Barrels per month) A 350 ( Nebraska B Sooo (B virginia Monthly demand (in Barrels) 1520 1700 Depots (1) Tennessee Georgia (3) North Carolina L042 South Carolina (5) Colorado utah 1400 950 11 so 1300 lost per Barrel to Shep to refinery from/to to (sepor) (Refinery ) 1 2 3 4 8 6 Cost pe banes to ship refinery (in $) t A 115 $1.35 $ 1.60 1.45 1-80 r15 B 11.25 +1.65 1:40 1.55 1:20 1.65 I All we red is a Q food at les 0 Decision Variable objective function constraints

0 becision variable i To formulate this problem as an Lp we begin by defining variable for each deusion that Exxon must make tij Number (Barrels per months sent from refinery i to depori where, (i=1,2, & j = 1,2,3,4,5,6) or shipping Total cost of supplying from the refineries to depott. V 1.50x, f 1.35 42 p 1.60%, 3 f 1.45414 + lesonis 1 1.75*,6 (lost og slepping from refinery A to depots) + 1.15X21 f 1.65*2 2 + 1.40*23 +1.55*24t 1. 2012, p 1.65*26 (cost of stepping from refinery B to depors) @ Objective function our objective is to minimize the shipping cost the from refinerics to depon. A Hince, the objective function is : Minimize z or Min z = lorox, p 1.35*12 1 1.60*, t 1.45 af 1. sonst 175416 + 1.25m + 1.65921 1.404 31 1.55*24 1 1. 2014 11.65*26

constraints @i, fupply constraino хи 1 ч, * * * * * * * * 2 35% 3.500 (refinery & Caltain) 1 3, 4 А (ора , ( di bn C.) ұшә to store undishbur full) &milarly Хя * * <t x,41 1 * 2 3 3 (Refinery B B constrains chy Demand constraints ху t и 7 15 Deman Constrains ( for depor 1) ( и и Ұі, 1, 7, Ijo -) * 3 1 x,3 7, 14 00 (у 2) 1 1 1,4 1 4 7 4 ут (v 4) іх : 7, 1| ут (и х) x. + х 7, 13 11 1, 4 ) Because all the ра xey's ( »), , 8 (?), 2, 3, 4, 5, 4 ) non-regatire teney we add the 4 mzhm 4 ; 7, о (1,2, i:1, 2, 24, 3, 4 )

to 1. хъ x f ( 58 х 1 (- 6o x,, 1 (+ 4 x x4 f 1-ихт 1 Combining The objective function and all constraints, The following following up Lp formulation Lp model minimize and monthly -Тргу Ски + Exxo w Posh : Min Za 1-17 хү6 1 1. Уку 1 1. К, 11, до хъ 1 | : у 11: их х 1. 6x xx С.Е. * * * * * * * * * * * * 30 бу Constraints) Хи 1 1 3 1 14 frt xx 2 ) all + x , 15 (Demand constraints) * * x 170 *ъt , , 14 х+14 4 у. Чst * 7, 11 ST Чь t , 7/ 12 Зү 7, о (4, 1,4 1, 1, 3, 4 ) (Any)