ISE 421 Operations Research 2 Exam 3 Sample

  1. Consider the multiple variable function
    f(X)=3x21 + 2x22 + x23 + x1 x2 x3 + 4x1 x3 + 5x2
    Classify the following points as minimum, maximum, inflection point, or regular point:
    1. X1=(0,-5/4,0)
    2. X2=(1,0,0)
  2. Assume that we want to find the economic order quantity for the average total cost function f(Q)= 400/Q+3/2 Q. We know that the optimal Q must lie in the uncertainty interval [10, 20]. Apply two complete iterations of the golden section search to sufficiently reduce the interval of uncertainty; and write the final interval.
  3. We seek to find the minimizer of the two-variable function f(X) = x21 + 4x22 - 8x1 - 16x2 We will start from X0 = (0,0). Apply a one iteration of the gradient method to find X1.

Instructor: Dr Muhammad Al-Salamah