A metal producing company wishes to blend a new allow that consists of 40 percent tin, 35percent zinc, and 25 percent lead. They will select a combination of the alloys available in thetable with the indicated percentages and costs per lb. Formulate and solve for the minimumcost to produce 110 lbs of the new alloy?Property\...1percent tin60percent zinc10percent lead 30Cost (Dollar/lb)Alloy2 3 4525 45 205015 45 504060 10 301077 74 88 84 94The minimum cost is 83---

Answered: A metal producing company wishes to…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

100%

A metal producing company wishes to blend a new allow that consists of 40 percent tin, 35
percent zinc, and 25 percent lead. They will select a combination of the alloys available in the
table with the indicated percentages and costs per lb. Formulate and solve for the minimum
cost to produce 110 lbs of the new alloy?
Property\...
1
percent tin
60
percent zinc
10
percent lead 30
Cost (Dollar/lb)
Alloy
2 3 4
5
25 45 20
50
15 45 50
40
60 10 30
10
77 74 88 84 94
The minimum cost is 83
---

Expert Solution

Objective Functions and Constraints:

Objective Functions and Constraints:

Based on the given details, the objective functions and constraints are

Objective Function:

$Min C = 77 x_{1} + 74 x_{2} + 88 x_{3} + 84 x_{4} + 94 x_{5}$

Constraints:

Subject to

$Tin : 60 % x_{1} + 25 % x_{2} + 45 % x_{3} + 20 % x_{4} + 50 % x_{5} = 40 % * 110 Zinc : 10 % x_{1} + 15 % x_{2} + 45 % x_{3} + 50 % x_{4} + 40 % x_{5} = 35 % * 110 Lead : 30 % x_{1} + 60 % x_{2} + 10 % x_{3} + 30 % x_{4} + 10 % x_{5} = 25 % * 110 Non Negativity : x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$