Dont Drink And Drive Brewery (DDAD) produces beer and ale. Beer sells for $5.70 per barrel, and ale sells for $2.05 per barrel. Producing a barrel of beer requires 5 pounds of corn and 2 pounds of hops. Producing a barrel of ale requires 2 pounds of corn and 1 pound of hops. Operational costs are $0.25 for a barrel of beer and $0.10 for a barrel of ale. The brewery has 12,000 pounds of corn and 6,000 pounds of hops. DDAD wants to maximize its profit.

a) Find the optimal production plan that maximizes the revenue.

b) What is (are) the bottleneck resource(s) for the brewery? Why?

c) If additional corn is available at 1.25 $/pound, should DDAD purchase any? Why or why not?

d) What should be the minimum selling price of ale, so that its production becomes profitable?

e) Suppose management dictates that at least one third of the total production must be ale. Write this new requirement as a linear mathematical expression. Find the new optimal solution with this additional constraint. What happened to the objective function? Did it improve or not?