6. (10 pts) A steel company uses coal, iron, and labor to produce three types of steel. The inputs and sales price for each type is shown in the following table. Steel 1 Steel 2 Steel 3 Coal Required 3 tons 2 tons 1 ton Iron Required 1 ton 0 tons 1 ton Labor Required Sales Price 1 hour $51 1 hour $30 1 hour $25 Up to 200 tons of coal can be purchased at a price of S10 per ton. Up to 60 tons of iron can be purchased at 88 per ton, and up to 100 hours of labor can be purchased at $5 per hour. a) What is the standard format for maximum profit? (2 points) b) What is the total profit? What is the production mix? (2 points) c) What does the profit of Steel 3 need to be for the company to produce any? Why? (2 points) d) If they could purchase a ton of coal for $2, should they do so? Why? (2 points) e) Shadow price of iron is S.50. What happens if they have 10 more tons of iron? (2 points) 6. (10 pts) A steel company uses coal, iron, and labor to produce three types of steel. The inputs and sales price for each type is shown in the following table. Steel 1 Steel 2 Steel 3 Coal Required 3 tons 2 tons 1 ton Iron Required 1 ton 0 tons 1 ton Labor Required Sales Price 1 hour $51 1 hour $30 1 hour $25 Up to 200 tons of coal can be purchased at a price of S10 per ton. Up to 60 tons of iron can be purchased at 88 per ton, and up to 100 hours of labor can be purchased at $5 per hour. a) What is the standard format for maximum profit? (2 points) b) What is the total profit? What is the production mix? (2 points) c) What does the profit of Steel 3 need to be for the company to produce any? Why? (2 points) d) If they could purchase a ton of coal for $2, should they do so? Why? (2 points) e) Shadow price of iron is S.50. What happens if they have 10 more tons of iron? (2 points)