Problem 2. [25 points] You are given the following data for a linear programming problem where the objective is to minimize the cost of conducting two nonnegative activities such that three benefits will not fall below their minimum acceptable levels. (a) Formulate a linear programming model for this problem. (b) Use the graphical method to solve this model. 1 (c) Identify the sensitivity range of the unit cost of activity 1 . Please calculate the optimal objective value if we change the unit cost of activity 1 to 80 . What if we change the unit cost of activity 1 to 90 ? (d) Identify the sensitivity range of the minimum acceptable level of benefit 3 . Please calculate the optimal objective value if we change the minimum acceptable level of benefit 3 to 130 . What if we change the minimum acceptable level of benefit 3 to 110 ? (e) Identify the sensitivity range of the unit cost of activity 2 . Suppose we change the unit cost of the two activities to 90 for activity 1 and 80 for activity 2 , are the new unit costs in the sensitivity range? Will the optimal solution change? Is the sensitivity range applicable when multiple parameters change simultaneously