Q. 3. Recall the Blending (1) problem that was formulated in class. In this prob- lem, a refinery distills crude petroleum obtained from two sources, Saudi Arabia and Venezuela, into three main products: gasoline, jet fuel and lubricants. The two crudes differ in chemical composition and therefore, yield different product mixes. Each ton of Saudi crude yields 0.3 ton of gasoline, 0.4 ton of jet fuel and 0.2 ton of lubricants. Each ton of Venezuelan crude yields 0.4 ton of gasoline, 0.2 ton of jet fuel and 0.3 ton of lubricants. The remaining 10% of each ton is lost in refining. The crudes also differ in cost and availability. The refinery can purchase up to 90 tons per day from Saudi Arabia at $600 per ton. Up to 60 tons per day of Venezuelan crude is available at $550 per ton. The refinery's contracts with independent distributors require that it produce at least 20 tons per day of gasoline, 15 tons per day of jet fuel, and 5 tons per day of lubricants. How can these requirements be fulfilled most efficiently? The refinery's decision problem is formulated as a linear programming problem as follows: Let, 11 and 22 denote the tons of Saudi and Venezuelan crude refined per day. The model: min 600x1 + 550:22 s.t. 0.321 +0.4.02 > 20 0.421 +0.2.2 > 15 0.201 + 0.322 > 5 21 0 (a) Use the graphical method and show all the feasible solutions to the refinery's decision problem. Mark all the extreme points clearly. (b) Identify the optimal solution, i.e., the optimal value of 21 and 22. What is the optimal cost? (c) What is the minimum amount by which the cost of Venezuela crude should de- crease for the optimal solution in b) to move to a new extreme point? Show all your calculations. (d) What is the minimum amount by which the daily requirement of lubricant (which is currently 5 tons) must increase to for the optimal solution to change? Show