Question

Bloomington Brewery produces beer and ale. Beer sells for $5 per barrel, and ale sells for $2 per barrel. Producing a barrel of beer requires 5 lb of corn and 2 lb of hops. Producing a barrel of ale requires 2 lb of corn and 1 lb of hops. 60 lb of corn and 25 lb of hops are available. Formulate an LP that can be used to maximize revenue. Solve the LP graphically.

Answer 1

The answer is below

Step-by-step explanation:

Let x represent the amount of beer sold and y represent the amount of ale sold. The revenue of selling x barrels of beer is 5x and selling y barrels of ale is 2y hence the total revenue = 5x + 2y. If z represent the maximum revenue then:

z = 5x + 2y

Since 60 lb of corn is available and beer requires 5 lb of corn while ale require 2 lb of corn hence:

5x + 2y ≤ 60

Also, 25 lb of hops is available and beer requires 2 lb of hops while ale require 1 lb of hops hence:

2x + y ≤ 25

Also x > 0 and y > 0

The LP is:

z = 5x + 2y

5x + 2y ≤ 60

2x + y ≤ 25

x > 0 and y > 0

Using geogebra graphing, the maximum revenue is at (0, 30)

Hence:

z = 5x + 2y = 5(0) + 2(30) = 60

The maximum revenue is 60