The Clarkson Coffee Company produces two grades of coffee, the Superb blend and the Run-of-the-Mill blend....

 

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The Clarkson Coffee Company produces two grades of coffee, the Superb blend and the Run-of-the-Mill blend. Three types of coffee beans are combined to produce these blends. The availability and cost of these beans for the upcoming month are shown in the table below: Typeof Coffee Bean Cost($ per thousand pounds) Availability(thousands of pounds) A B C $2,500 $2,000 $1,400 700 900 800 In addition to the limitations of raw material availability, the company must satisfy a set of quality control restrictions. The Superb blend, which sells for $3,000 per thousand pounds, must contain at least fifty percent Type A beans and no more than twenty percent Type C beans. The Run-of-the-Mill blend, which sells for $1,800 per thousand pounds, must contain at least thirty percent Type A beans and no more than sixty percent Type C beans. Also, to have a more balanced production, they want to make sure Superb blend production does not exceed Run-of-the-Mill production by more than 500 pounds. The Clarkson Coffee Company would like to determine how many thousands of pounds of each type of bean to purchase so as to maximize profit from the resulting mixes of the two blends. a. Formulate an LP model for this problem. b. Make a spreadsheet model for this problem and solve it using Solver. Report the optimal solution (i.e. values for all the decision variables) The Clarkson Coffee Company produces two grades of coffee, the Superb blend and the Run-of-the-Mill blend. Three types of coffee beans are combined to produce these blends. The availability and cost of these beans for the upcoming month are shown in the table below: Typeof Coffee Bean Cost($ per thousand pounds) Availability(thousands of pounds) A B C $2,500 $2,000 $1,400 700 900 800 In addition to the limitations of raw material availability, the company must satisfy a set of quality control restrictions. The Superb blend, which sells for $3,000 per thousand pounds, must contain at least fifty percent Type A beans and no more than twenty percent Type C beans. The Run-of-the-Mill blend, which sells for $1,800 per thousand pounds, must contain at least thirty percent Type A beans and no more than sixty percent Type C beans. Also, to have a more balanced production, they want to make sure Superb blend production does not exceed Run-of-the-Mill production by more than 500 pounds. The Clarkson Coffee Company would like to determine how many thousands of pounds of each type of bean to purchase so as to maximize profit from the resulting mixes of the two blends. a. Formulate an LP model for this problem. b. Make a spreadsheet model for this problem and solve it using Solver. Report the optimal solution (i.e. values for all the decision variables)

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To formulate an LP model for this problem we need to define the decision variables objective functio... View the full answer