Write the problem in standard form. Identify slack/surplus variables. The optimal solution of the above LP model is (180/7, 150/7). What are the values of the slack and surplus variables at the optimal solution?

Problem Solving

1. Consider the following linear programming problem:

Min

s.t.

• Write the problem in standard form. Identify slack/surplus variables. (10 points)
• The optimal solution of the above LP model is (180/7, 150/7). What are the values of the slack and surplus variables at the optimal solution? (12 points)

2.Consider the following linear programming problem:

Max

s.t.

• Identify the feasible region. (12 points)
• Are any of the constraints redundant?  If yes, then identify the constraint that is redundant. (10 points)
• Find all the extreme points – list the value of x₁ and x₂ at each extreme point. (6 points)
• What is the optimal solution? (5 points)

3. RVW (Restored Volkswagens) buys 15 used VW’s at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with.  When they are restored to RVW’s specifications, RVW sells 10 each to three different used car lots.  There are various costs associated with the average purchase and transportation prices from each auction to each repair shop.  Also there are transportation costs from the repair shops to the used car lots.  RVW is concerned with minimizing its total cost given the costs in the table below.

• Given the costs below, draw a network representation for this problem. (10 points)

• Formulate this problem as a linear programming model. (15 points)

(Note: You do not need to solve the model.)