Question

the black jack distillery produces custom blended whiskey. a particular blend consists of rye and bourbon whiskey. the company has received an order for a minimum of 400 litres of the custom blend. the customer also specified that the prder must contain at least 40% rye and not more then 250 litres of bourbon. the customer also specified that the blend should be mixed in the ratio of two parts rye to one part bourbon. the distillery can produce 500 litres per week, regardless of the blend. the production manager wants to complete the order in one week the. the blend is solk for 12 per litre. the distilerry companys cost per gallon cost per gallon is 4 for rye and 2 for bourbon. the company wants to determine the blend mix that will meet customer requirements and max profits formulate and solve a linear programming model for this problem solve the problem using graphical method

Answer 1

Let 'R' and 'B' be the liters of Rye and Bourbon mixed in order to produce the final product.

Objective Function: Maximize Z = total profit
Z = 12*(R+B) - 4*R - 2*B = 8R + 10B

Subject to,

R >= 40%*(R+B) or, 0.6R - 0.4B >= 0

R + B >= 400

B <= 250

R/B = 2/1 or, R - 2B = 0

R + B <= 500

R, B >= 0

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Implementation

Optimal Solution

R = 333.33 litre
B = 166.67 litre