1. The Metalco Company desires to blend a new alloy of 40 percent tin, 35 percent zinc, and 25 percent lead from several available alloys having the following properties:

Property

Alloy

1

2

3

4

5

Percentage of Tin

60

25

45

20

50

Percentage of Zinc

10

15

45

50

40

Percentage of Lead

30

60

10

30

10

Cost($/lb.)

22

20

25

24

27

The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a minimum cost. (a) Formulate a linear programming model for this problem. Clearly state the choice variables, objective function and the constraints. (b) Solve this model by using MS excel. (c) Generate the sensitivity report and interpret all the shadow prices. (d) If the desired zinc and lead portion is changed to 25% and 35%, are these shadow prices still valid? Show using the 100% rule.

The Metalco Company desires to blend a new alloy of 40 percent tin, 35 percent zinc, and 25 percent lead from several available alloys having the following properties: Property Alloy 1 2 3 4 5 Percentage 60 25 45 20 50 of Tin Percentage 10 15 45 50 40 of Zinc Percentage 30 60 10 30 10 of Lead Cost($/lb.) 22 20 25 24 27 The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a minimum cost. (a) Formulate a linear programming model for this problem. Clearly state the choice variables, objective function and the constraints. (b) Solve this model by using MS excel. (c) Generate the sensitivity report and interpret all the shadow prices. (d) If the desired zinc and lead portion is changed to 25% and 35%, are these shadow prices still valid? Show using the 100% rule