Point values are as indicated. As always, you must show your work to receive more than half credit.

1. In some situation you know that , while both
   . For each of the following two functions, find the maximum possible value and the coordinates of the corner point where the maximum occurs:

   
   
   

2. Compute each of the following which is possible to compute. For any which are impossible explain why.

   
   
   

3. For a large fundraising party, you are making sixty-four gallons of a punch which is 18% alcohol. You have 10 gallons of an alcohol free juice mixture and must add as much vodka (40% alcohol) and wine (12% alcohol) as necessary. How much of the vodka and wine do you need.
   1. Set up this problem as a system of linear equations.
   2. Write it in matrix form.
   3. Solve using matrix row operations.

4. Perform (and indicate as you do them) whatever row operations are needed to convert the following matrix to reduced form:
   

5. BONUS - 20 quiz points

   The random variable X takes on the values 1,2, and 3 with probabilities p, q,and r respectively. If E(X) = 5/3 and E(X ³) = 23/3, find E(X ²).