Stats Solutions

(Solution Library) Consider the following LP problem: Maximize profit = 10X 1 + 8X 2 Subject to: 4X 1 + 2X 2 < 80 X 1 + 2X 2 < 50 X 1 , X 2 > 0 Solve the

Question: Consider the following LP problem:

Maximize profit = 10X 1 + 8X 2

Subject to: 4X 1 + 2X 2 < 80

X 1 + 2X 2 < 50

X 1 , X 2 > 0

  1. Solve the problem graphically
  2. Set up the initial simplex tableau. On the graph identify the corner point represented by this tableau.
    Cj $10 $8 $0 $0
    Solution
    Mix X 1 X 2 S 1 S 2 Qty
    $0 S 1 4 2 0 0 80
    $0 S 2 1 2 0 0 50 Zj $0 $0 $0 $0
    Cj-Zj $10 $8 $0 $0
  3. Select the pivot column. Which variable is entering variable.
  4. Compute the ratio of the quantity to pivot column substitution rate for each row. Identify the points on the graph related to these ratios.
  5. How many units of the entering variable will be brought into the solution in the second tableau? 20 What would happen if the largest ratio rather than the smallest ratio were selected to determine this (see the graph)?
  6. Which variable is the leaving variable? S 1 What will the value of this variable be in the next tableau?
  7. Finish solving this problem using the simplex algorithm.
  8. The solution in the simplex tableau is a corner point on the graph. Identify the corner point associated with each tableau.

Price: $2.99
Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document


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