Beerco manufactures ale and beer from corn hops and malt Cur

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.

a) (4 points) Graphically find the range of values for the price of ale for which the current basis remains optimal.

b) (4 points) Graphically find the range of values for the price of beer for which the current basis remains optimal.

c) (4 points) Graphically find the range of values for the amount of available corn for which the current basis remains optimal. What is the shadow price of the corn constraint?

d) (4 points) Graphically find the range of values for the amount of available hops for which the current basis remains optimal. What is the shadow price of the hops constraint?

e) (4 points) Graphically find the range of values for the amount of available malt for which the current basis remains optimal. What is the shadow price of the malt constraint?

Solution