Tarmac Chemical Corporation produces a special chemical compound - called CHEMIX - that is used extensively in high school chemistry classes. This compound must contain at least 20% sulfur, at least 30% iron oxide, and at least 30% but no more than 45% potassium. Tarmac's marketing department has estimated that it will need at least 600 pounds of this compound to meet the expected demand during the coming school session. Tarmac can buy three compounds to mix together to produce CHEMIX. The makeup of these compounds is shown in the table. Compounds 1, 2, and 3 cost $5.00, $5.25, and $5.50 per pound, respectively. Tarmac wants to use an LP model to determine the least costly way of producing enough CHEMIX to meet the demand expected for the coming year. a. What is the optimal solution? Use Solver to create a Sensitivity Report and answer the following questions: b. Suppose the cost of the first two compounds increases by $1.00 per pound and the cost of the third compound increases by $0.50 per pound. Does the optimal solution change? c. How does the solution change if the maximum amount of potassium allowed decreases from 45% to 40%? d. How much does the cost of the mix increase if the specifications for CHEM1X change to require at least 31% sulfur? (Hint: Remember that the shadow price indicates the impact on the objective function if the RHS value of the associated constraint increases by 1.) Compound Sulfur Iron Oxide Potassium Cost 1 20% 60% 20% $5.00 2 40% 30% 30% $5.25 3 10% 40% 50% $5.50

Tarmac Chemical Corporation produces a special chemical compound - called CHEMIX - that is used extensively in high school chemistry classes. This compound must contain at least 20% sulfur, at least 30% iron oxide, and at least 30% but no more than 45% potassium. Tarmac's marketing department has estimated that it will need at least 600 pounds of this compound to meet the expected demand during the coming school session. Tarmac can buy three compounds to mix together to produce CHEMIX. The makeup 5 of these compounds is shown in the table. 7 Compounds 1, 2, and 3 cost $5.00, $5.25, and $5.50 per pound, respectively. Tarmac wants to use an LP 3 model to determine the least costly way of producing enough CHEMIX to meet the demand expected for the coming year. 0 1 a. What is the optimal solution? 2 Use Solver to create a Sensitivity Report and answer the following questions: 3 b. Suppose the cost of the first two compounds increases by $1.00 per pound and the cost of the third 4 compound increases by $0.50 per pound. Does the optimal solution change? c. How does the solution change if the maximum amount of potassium allowed decreases from 45% to 6 40%? 8 7 d. How much does the cost of the mix increase if the specifications for CHEM1X change to require at least 31% sulfur? (Hint: Remember that the shadow price indicates the impact on the objective function if the RHS value of the associated constraint increases by 1.) 9 0 1 2 3 Compound Sulfur Iron Oxide Potassium Cost 456 7 1 20% 60% 20% $5.00 23 40% 30% 30% $5.25 10% 40% 50% $5.50