4. A car factory makes 4,6 and 8 cylinder cars. Assume each 4 cylinder car gets 50 miles per gallon (mpg ), requires 20m2 of steel and yields a profit of $600. Each 6 cylinder car gets 30mpg, requires 10 m2 of steel and yields a profit of $300. Each 8 cylinder car gets 25mpg, requires 16m2 of steel and yields a profit of $500. Because of an EPA regulation, the cars made must average at least 35mpg. Each car requires 2 airbags. There are 600 airbags and 4,400m2 of steel available. In problem 2 in Assignment 2 , you used the simplex method to find how many cars of each type should be made to yield the maximum possible profit: Now, assume that the amount of steel available is a parameter that can be changed, and everything else in the problem remains the same. (a) (8 marks) Use a sensitivity analysis to determine the shadow price (which can also be called the marginal value) of the steel and the feasibility range for this shadow price. (b) (10 marks) Draw a graph showing the maximum profit versus the amount of steel available. (You will probably need to use more than one sensitivity analysis). (c) (8 marks) Draw a graph showing the shadow price of the steel as a function of the amount of steel available. Explain how your graph illustrates a "law of diminishing returns