Question

Bloomington Breweries produces beer, ale, lager and a pilsner. Beer sells for $3 per barrel. Ale sells for $4 per barrel. Lager sells for $6 per barrel and Pilsner sells for $4.50 per barrel. The table below shows ingredient requirements (in lbs.) for each barrel of brewery type produced as well as availability of each ingredient. Assume all quantities of Pilsner produced can be sold but no more than 50,000 barrels of each Ale and lager can be sold and at least 30,000 barrels of beer must be sold. Formulate an LP problem to maximize brewery sales, explain objextive and constraints equations and solve

	Requirements
Ingredient	Beer	Ale	Lager	Pilsner	Amount Available (in lbs.)
Corn	5	4	6	4	700000
Malt	1	2	3	2	500000
Hops	2	3	3	3	500000

Answer 1

beer - x ale - y, Lager - z Pilsner - w

maximize z = 3x+ 4y+ 6z + 4.5w

x >= 30000

y <= 50000, z<= 50000

5x+4y+6z+4w<= 700000

x+2y+3z+2w<= 500000

2x+3y+3z+3w<= 500000

Solving in excel

Ingredient	Beer	Ale	Lager	Pilsner	Amount Available (in lbs.)
	30000.02	0	0	137500
Corn	5	4	6	4	700000	700000
Malt	1	2	3	2	500000	304999.9748
Hops	2	3	3	3	500000	472499.9706
	3	4	6	4.5		708749.956

Ingredient	Beer	Ale	Lager	Pilsner	Amount Available (in lbs.)
	30000.0167762109	0	0	137499.979027588
Corn	5	4	6	4	700000	=SUMPRODUCT($B$2:$E$2,B3:E3)
Malt	1	2	3	2	500000	=SUMPRODUCT($B$2:$E$2,B4:E4)
Hops	2	3	3	3	500000	=SUMPRODUCT($B$2:$E$2,B5:E5)
	3	4	6	4.5		=SUMPRODUCT($B$2:$E$2,B7:E7)

X = 30000

Y = 0

z = 0

W = 137500