Beerco manufactures ale and beer from corn, hops, and malt. Currently, 40 lb of corn, 30 lb of hops, and 40 lb of malt are available. A barrel of ale sells for $40 and requires 1 lb of corn, 1 lb of hops, and 2 lb of malt. A barrel of beer sells for $50 and requires 2 lb of corn, 1 lb of hops, and 1 lb of malt. Beerco can sell all ale and beer that is produced. Assume that Beerco's goal is to maximize total sales revenue and solve the following LP:
max z = 40ALE + 50BEER
s.t. ALE + 2BEER <= 40 (Corn constraint)
ALE + BEER <= 30 (Hops constraint)
2ALE + BEER <= 40 (Malt constraint)
ALE, BEER >= 0
ALE = barrels of ale produced and BEER = barrels of beer produced.
z Ale Beer s1 s2 s3 RHS
1 0 0 20 0 10 1200
0 0 1 2/3 0 - 1/3 40/3
0 0 0 - 1/3 1 - 1/3 3 1/3
0 1 0 - 1/3 0 2/3 40/3
a. Find the range of values for the price of ale for which the current basis remains optimal.
b. Find the range of values for the price of beer for which the current basis remains optimal.
C. Find the range of values of the amount of available corn for which the current basis remains optimal.
d. Find the range of values of the amount of available hops for which the current basis remains optimal.
e. Find the range of values of the amount of available malt for which the current basis remains optimal.