An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file P04_78.xlsx. Gasoline sells for $75 per barrel. Gasoline can have a density of at most 0.95 units per barrel, a viscosity of at most 35 units per barrel, and a sulfur content of at most 3.3 units per barrel. a. How can the company maximize its profit? b. Describe how the optimal solution to the problem changes as the price of gasoline ranges from $65 to $85 per barrel.

I need step by step

2)
Selling price per barrel	75
Input	Cost	Density	Viscosity	Sulfur
Light gas oil	$69.50	0.83	40	1.00
Heavy gas oil	$66.70	0.88	26	2.20
Waxy Distilate	$56.40	0.92	30	2.80
Atmospheric Residue	$16.50	0.97	65	4.10
Vaccum Residue	$10.40	1.50	48	5.00
Upper Limit		0.95	35	3.30
Blending Plan (1000s barrell)
Input	Inputs used		Inputs available
Light gas oil	0	<=	40,000
Heavy gas oil	0	<=	50,000
Waxy distilate	0	<=	70,000
Atmospheric residue	0	<=	60,000
Vaccum residue	0	<=	80,000
Input Sum	0		300000
Constraints	Dentisty	Viscosity	Sulfur
Actual	0	0	0
	<=	<=	<=
Max
Cost	$0.00	Revenue	0
Profit	$0.00