Question

Consider a refinery that produces three types of motor oil: Standard, Ex- tra, and Super. The selling prices are $9.00, $13.00, and $19.00 per barrel respectively. These oils can be made from three basic ingredients; crude oil, paraffin, and filler. The costs of the ingredients are $19.00, $9.00 and $11.00 per barrel, respectively. Company engineers have developed the following specifications for each oil Standard-60% paraffin, 40% filler Extra-at least 25% crude oil and no more than 45% paraffin Super-at least 50% crude oil and no more than 25% paraffin The CO2 emissions of Standard, Extra, and Super oils are 13.0, 11.8, and 8.0 units per barrel. With a supply capacity of 110, 90, and 70 thou- sand barrels per week for crude oil, paraffin, and filler, what should be blended in order to maximize profits as well as satisfy the requirements of the EPA to minimize the CO2 emissions from all the products of this industry? Solve the problem using the goal programming approach, if th goals are to have a profit greater than or equal to $5 per barrel and CO2 emissions less than or eaual to 10 units per barrel

Answer 1

Answer :

	standard	standard	extra	extra	extra	super	super	super
	Paraffin	Filler	Crude oil	Paraffin	Filler	Crude oil	Paraffin	Filler	d1-	d1+	d2-	d2+
DV	38571	25714	0	0	0	110000	51429	44286	532857	0	218571	0
OF									1			1	532857
Selling price	9	9	13	13	13	19	19	19
Cost	9	11	19	9	11	19	9	11
profit (goal 1)	-5	-7	-11	-1	-3	-5	5	3	1	-1			-4.65661E-10	=	0
CO2 (Goal 2)	3	3	1.8	1.8	1.8	-2	-2	-2			1	-1	2.91038E-11	=	0
Standard Mix	0.4	-0.6											-1.63709E-11	=	0
Extra Mix 1			-0.75	0.25	0.25								2.27374E-11	<=	0
Extra Mix 2			-0.45	0.55	-0.45								5.00222E-11	<=	0
Super Mix 1						-0.5	0.5	0.5					-7142.857143	<=	0
Super Mix 2						-0.25	0.75	-0.25					-4.36557E-11	<=	0
Capacity crude oil			1			1							110,000	=	110,000
Capacity paraffin	1			1			1						90,000	=	90,000
Capacity filler		1			1			1					70,000	=	70,000

So, although the CO₂ goal was achieved, the profit goal was underachieved.