Q2 (26 points). Considering the same background information discussed in the refinery business case, the refinery business transforms two types of crude oil (heavy and light) into higher value refined petroleum products (gasoline, diesel, and others). Three pieces of equipment are needed to refine crude oil: distillation equipment, conversion equipment, and blending equipment. The following updated information has been provided by the president of the company after renegotiating contracts with their current suppliers and distributors: Table 1 Updated output unit price charged to distributors End products Unit price (gallons) Gasoline 3/gallon Diesel 2.5/gallon Other 2/gallon Table 2 Updated per barrel price paid to the supplier Light crude Heavy crude Price $75/barrel $70/barrel Current production policy is to process 600,000 barrels of light crude oil and 200,000 barrels of heavy crude oil. All other information regarding production (crude input and output, refining equipment demand per 1,000 barrels, weekly available equipment hours, fixed overhead, variable overhead, and labor costs) stay the same (as described in the case). Based on the updated information, the president would like to know whether the current production policy is optimal. Please use Solver Simplex LP (as discussed in class) to answer the following questions: 1. What is the per barrel contribution for each type of crude oil? 2. What is the total profit under the current production policy? Hint: Total profit = [total contribution] - [fixed overhead] 3. Assuming the goal is to maximize total contribution, how many barrels of each type of crude should the refinery produce? Hint: two types of constraints need to be imposed (resource constraint and non-negativity constraint). 4. What is the new total contribution and the new profit with the optimal input mix? 5. How much more contribution can the refinery add if available equipment hour per week for blending equipment increases by 200 hours, when keeping all other parameters unchanged