Problem 4. Throughout this course, we have defined dual problems using standard form due to our focus on the simplex algorithm, which requires standard form. There are other formulations for linear optimization problems, which we consider in this exercise. Consider the following two problems: Notice how these are different from the standard form that we have discussed in this class. (a) Convert Problem A into standard form. (b) Convert Problem B into standard form. (c) Using the definition of a dual problem, show that your results in parts (a) and (b) are dual problems of one another. You may find block matrices helpful for this. Note: From this, we see that Problem A and Problem B are dual to each other. As you may expect, there are versions of Weak Duality, Strong Duality, and Complementary Slackness for these two problems, which you can directly derive using the versions that we have established