Question

1. Problem 9-15 (Algorithmic)

   Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 92 while super must have a level of at least 100. The cost per barrel, octane levels, and available amounts (in barrels) for the upcoming two-week period are shown in the following table. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown.

   Input	Cost/Barrel	Octane	Available (barrels)
   1	$16.5	95	140000
   2	$15	86	325000
   3	$15.5	105	300000

   	Revenue/Barrel	Max Demand (barrels)
   Regular	$18.5	320000
   Super	$20	450000

   Develop and solve a linear programming model to maximize contribution to profit.

   Let	Ri = the number of barrels of input i to use to produce Regular, i=1,2,3
   	Si = the number of barrels of input i to use to produce Super, i=1,2,3

   If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

   Max

   _R1

   +

   _R2

   +

   _R3

   +

   _S1

   +

   _S2

   +

   _S3

   s.t.

   _R1

   +

   _S1

   ≤

   _

   _R2

   +

   +

   _S2

   ≤

   _

   _R3

   +

   S3

   ≤

   _

   _R1

   +

   _R2

   +

   _R3

   ≤

   _

   _S1

   +

   _S2

   +

   _S3

   ≤

   _

   _R1

   +

   _R2

   +

   _R3

   ≥

   _R1

   +

   _R2

   +

   _R3

   _S1

   +

   _S2

   +

   _S3

   ≥

   _S1

   +

   _S2

   +

   _S3

   R1, R2, R3, S1, S2, S3 ≥ 0

   What is the optimal contribution to profit? _

   Maximum Profit = _$   by making _ barrels of Regular and _ barrels of Super.

Answer 1

Max z
= (R1+ R2 + R3) 18.5 + (S1 +S 2 + S3)*20 -
16.5 (R1 + S1) - 15 (R2 + S2) - 15.5 (R3 + S3)

2 R1 + 3.5 R2 + 3 R3 + 3.5 S1 + 5 S2 + 4.5 S3
CONSTRAINTS

R1 + S1 <= 140000
R2 + S2 <= 325000
R3 + S3 <= 300000

R1+R2 + R3 <= 320000
S1 + S2 + S3 <= 450000

95 R1 + 86 R2 + 105 R3 >= 92(R1 + R2 + R3)
95 S1 + 86 S2 + 105 S3 >= 100(S1 + S2 +S3)

2	_R1	3.5	_R2	3	_R3	3.5	_S1	5	_S2	4.5	_S3
s.t.
1	_R1					1	_S1					≤	140000
		1	_R2	+				1	_S2			≤	325000
				1	_R3					1	S3	≤	300000
1	_R1	1	_R2	1	_R3							≤	320000
						1	_S1	1	_S2	1	_S3	≤	450000
95	_R1	86	_R2	105	_R3	≥92	_R1	92	_R2	92	_R3
95	_S1	86	_S2	105	_S3	≥100	_S1	100	_S2	100	_S3