A company produces beer and ale form hops. A gallon of beer requires 2 lb of California hops and 4 lb of Florida hops. A gallon of beer sells for $10 and costs $5 to produce. A gallon of ale requires 1 lb of California hops and 1 lb of Florida hops. A gallon of ale sells for $6 and costs $4 to produce. A total of 30 lb California hops and 50 lb of Florida hops are available. All beer and ale that is produced can be sold. Marketing considerations require that at least 11 gallons of beer produced. Formulate an appropriate linear program and solve it using WINQSB. Based only on the output, answer the following questions.
a. What would the company’s profit be if only 46 lb of Florida hops were available?
b. If a gallon of ale sold for only $5.50, what would be the new optimal objective value?
c. What would company’s profit be if at least 12 gallons of beer had to be produced?
d. What would company’s profit be if an additional constraint that required that the amounts of beer and ale to be produced were in a ratio of 11:6 was imposed?
e. Suppose that an additional 5 lb of Florida hops were available at a total cost of $5. Should the company obtain these? Explain
f. What will the optimal solution be if a gallon of beer required 2 lb of California hops and 5 lbs of Florida hops?