Statistics

  

1. Consider the following transportation problem. XYZ Company has capacities of 600 in its Corning plant and 200 in it plant in Geneva. However, its demands come from Fairport, Mendon, and Penfield at the following demand levels 300, 200, and 300 respectively.

The transportation costs per unit are as follows:

  

Fairport

Mendon

Penfield

 

Corning

16

10

14

 

Geneva

12

12

20

a) Develop a linear programming formulation of this transportation problem.

b) Use Excel Solver to solve this problem and find the optimal solution.

2. Consider the following linear program

Max 3x1 + 2x2

s.t.

1x1 + 1x2 < 10

3x1 + 1x2 < 24

1x1 + 2x2< 16

And x1, x2 > 0.

a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of x1, x2, and Z.

b) Assume that the objective function coefficient for x1 changes from 3 to 5. Does the optimal solution change? 

c) Assume that the objective function coefficient for x1 remains 3, but the objective function coefficient for x2 changes from 2 to 4. Does the optimal solution change?

d) What are the shadow prices for these constraints?

e) What conclusions can you draw about changes to the right hand side of constraint 2?

f) Identify the binding and non-binding constraints in this problem and explain.