Question 1129761: There are two principal ingredients in the mixture, both sources of protein: x1 and X2. The first source of protein X1 costs ₱30 a pound and the second, x2 costs ₱60 per pound. Chemical constraints dictate that the mixture contains not more than 4,000 pounds of X1 and must contain at least 2,000 pounds of X2. How many pounds of each ingredient must be utilized in order to minimize the cost? X1 is _____, X2 is _____, cost is _____
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are two principal ingredients in the mixture, both sources of protein: x1 and X2. The first source of protein X1 costs ₱30 a pound and the second, x2 costs ₱60 per pound. Chemical constraints dictate that the mixture contains not more than 4,000 pounds of X1 and must contain at least 2,000 pounds of X2.
Objective Function: Cost = 30X1 + 60X2
------
0<= X1 <= 4000
2000<= X2
----
Sketch the acceptable region limits: let X1 be the vertical axis;let X2 be the horizontal axis.
Sketch the horizontal line limit X1 = 4000
Sketch the vertical line limit X2 = 2000
Note: These line limits do not form a closed area.
Vertices to check in the Objective Function:: (2000,0);(2000,4000)
---
Using (2000,0) you get Cost = 30*0+60*2000 = $120000 (smaller cost)
Using (2000,4000) you get Cost = 30*2000+60*4000 = $300000
----
How many pounds of each ingredient must be utilized in order to minimize the cost? X1 is 0__, X2 is 2000, cost is $120,000_____
-----
Cheers,
Stan H.
---------
Answer by ikleyn(52880)  (Show Source):
You can put this solution on YOUR website! .
If you want to learn on how to solve such problems using the Linear Programming method, or if you want to see
other similar solved problems, look into the lesson
- Solving minimax problems by the Linear Programming method
in this site and into these links
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html
https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html
in this forum.
|
|
|
