Question 2 Consider a truck loading problem where there are two types of products. The mass, volume and profit of each unit of Product A and Product B are as follows: Product Type Mass/unit Volume/unit Profit/unit A 2kg $2 8d3 2003 B 10kg $3 Only one truck is available. The maximum volume of this truck is 15,000d3 and the loaded weight should be no greater than 6,000kg. The maximum amount of Products A and B are 1,800 and 700, respectively. (1) The truck owner wants to set up the optimal loading plan so that the total profit can be maximized. Write the LP formulation of this problem. (2) Solve this problem using the simplex method with the simplex tableau (Note that the number of iterations listed in the empty table in the Answer Sheet might not be the same as that in the optimal solution). (3) Now due to the uncertainty in market, the unit profit of Product B may be less than or greater than the expected unit profit. The truck owner wants to know in what range of Product B unit profit, the above loading plan remains optimal. (4) In order to increase the profit, the truck owner wants to increase the capacity of this truck. There are two enhancement strategies: a. Increasing the capacity in terms of mass, which will cost $0.2 for every 1kg increased, while the capacity in terms of volume remains the same; b. Increasing the capacity in terms of volume, which will cost $0.1 for every 1d3 increased, while the capacity in terms of mass remains the same. Which enhancement strategy is more cost-effective? You need to explain why. (5) Now there is another requirement that the amount of Product B must be at least 50 units. Write the new LP formulation to incorporate this requirement, and then transform this problem to its dual form. You do NOT need to solve this problem. Question 2 Consider a truck loading problem where there are two types of products. The mass, volume and profit of each unit of Product A and Product B are as follows: Product Type Mass/unit Volume/unit Profit/unit A 2kg $2 8d3 2003 B 10kg $3 Only one truck is available. The maximum volume of this truck is 15,000d3 and the loaded weight should be no greater than 6,000kg. The maximum amount of Products A and B are 1,800 and 700, respectively. (1) The truck owner wants to set up the optimal loading plan so that the total profit can be maximized. Write the LP formulation of this problem. (2) Solve this problem using the simplex method with the simplex tableau (Note that the number of iterations listed in the empty table in the Answer Sheet might not be the same as that in the optimal solution). (3) Now due to the uncertainty in market, the unit profit of Product B may be less than or greater than the expected unit profit. The truck owner wants to know in what range of Product B unit profit, the above loading plan remains optimal. (4) In order to increase the profit, the truck owner wants to increase the capacity of this truck. There are two enhancement strategies: a. Increasing the capacity in terms of mass, which will cost $0.2 for every 1kg increased, while the capacity in terms of volume remains the same; b. Increasing the capacity in terms of volume, which will cost $0.1 for every 1d3 increased, while the capacity in terms of mass remains the same. Which enhancement strategy is more cost-effective? You need to explain why. (5) Now there is another requirement that the amount of Product B must be at least 50 units. Write the new LP formulation to incorporate this requirement, and then transform this problem to its dual form. You do NOT need to solve this