Problem 4 Diageo is a company that specializes in producing Scotch and Irish Whi

Question

Problem 4 Diageo is a company that specializes in producing Scotch and Irish Whiskey. The raw material needed to produce the liquor is a specific variety of fermented grain mash that Diageo buys from specialized farmers. Each pound of the fermented grain mash can be purchased for $4. To produce the liquor, the fermented grain mash requires passing through a distillation process that takes 2 hours per pound and consumes 18 liters of water per pound. After the distillation process is completed, each pound of fermented mash yields two products, 3 liters of Scotch whiskey and 2 liters of Irish whiskey. Each liter of Scotch whiskey sells for $60 and each liter of Irish whiskey sells for $45 Suppose that Diageo has the option of aging some of the whiskey in oak casks mixed with some secret spices to produce luxury versions of the whiskey. Aging 1 liter of of Scotch whiskey requires 2 oz of spices and aging 1 liter of and Irish whiskey requires 3 oz of spices. Each liter of luxury Scotch whiskey sells for $120 and each liter of luxury Irish whiskey sells for $110 For the production process, suppose that you have available 6,000 liters of water, 800 hours available for the distillation process, and 300 oz of secret spices. Formulate a linear problem that allows you to determine a way for Diageo to maximize their profits. a) Write a formulation for this problem. Make sure you describe all the elements of your formulation (i.e., decision variables, parameters, constraints, and objective function)

Explanation / Answer

a) Formulation is following:

Decision variables:  Let G be the pounds of grain mash to be purchased,

S and R be the liters of Scotch and Irish whiskey to be sold, and

AS and AR be the liters of Scotch and Irish whiskey to be aged.

Parameters:  Selling price of Whiskeys (S =$ 60, R =$ 45, AS =$120, AR =$ 110, 2 hours and 18 liters of water required for distillation of each pound of grain mash, each pound of grain mash produces 3 liters of Scotch and 2 liters of Irish whiskey, Aging 1 liters of Scotch whiskey requires 2 oz of spices and aging 1 liter of Irish whiskey requires 3 oz of spices. 6000 liters of water, 800 hours for distillation process and 300 oz of spices are available.

Objective: Max 60S + 45R + 120AS + 110AR - 4G

Constraints:

S + AS = 3G

R + AR = 2G

2G <= 800

18G <= 6000

2AS + 3AR <= 300

G, S, R, AS, AR >= 0

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