You have two products, Alpha, and Beta. For every unit of Alpha, you make a $3...

 

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You have two products, Alpha, and Beta. For every unit of Alpha, you make a $3 profit and for every unit of Beta you make a $2 profit. There are 10 kilograms of steel available. Each unit of Alpha requires 1 kilogram, and each unit of Beta requires 1 kilogram of steel. There are 24 kilograms of aluminum available. Each unit of Alpha requires 3 kilograms, and each unit of Beta requires 1 kilogram of aluminum. There are 16 kilograms of copper available. Each unit of Alpha requires 1 kilogram, and each unit of Beta requires 2 kilograms of copper. You prepare the following linear program: Max 3A + $2B Subject to: 1A+ 1B < 10 Steel 3A + 1B < 24 Aluminum 1A + 2B < 16 Copper A, B > 0 Required: Solve the following problem. Print the Solver Sensitivity report. a) Calculate the optimal solution in quantities of the two products and total dollar profit. b) Which of the three constraints are binding? c) Assume that the profit per unit of Alpha increases from $3 to $5. The profit per unit of Beta is unchanged. Does the optimal solution change? Find the optimal solution in number of units and total profit? d) Assume that the unit profit for Alpha remains $3 but the unit profit for Beta increases from $2 to $4. Does the optimal solution change? Find the optimal solution in number of units and total profit? e) If the quantity of steel is increased from 10 to 11 kilograms, what is the effect (if any) of this change on overall profit? You have two products, Alpha, and Beta. For every unit of Alpha, you make a $3 profit and for every unit of Beta you make a $2 profit. There are 10 kilograms of steel available. Each unit of Alpha requires 1 kilogram, and each unit of Beta requires 1 kilogram of steel. There are 24 kilograms of aluminum available. Each unit of Alpha requires 3 kilograms, and each unit of Beta requires 1 kilogram of aluminum. There are 16 kilograms of copper available. Each unit of Alpha requires 1 kilogram, and each unit of Beta requires 2 kilograms of copper. You prepare the following linear program: Max 3A + $2B Subject to: 1A+ 1B < 10 Steel 3A + 1B < 24 Aluminum 1A + 2B < 16 Copper A, B > 0 Required: Solve the following problem. Print the Solver Sensitivity report. a) Calculate the optimal solution in quantities of the two products and total dollar profit. b) Which of the three constraints are binding? c) Assume that the profit per unit of Alpha increases from $3 to $5. The profit per unit of Beta is unchanged. Does the optimal solution change? Find the optimal solution in number of units and total profit? d) Assume that the unit profit for Alpha remains $3 but the unit profit for Beta increases from $2 to $4. Does the optimal solution change? Find the optimal solution in number of units and total profit? e) If the quantity of steel is increased from 10 to 11 kilograms, what is the effect (if any) of this change on overall profit?