Question 1058344: Lumber Company can convert logs into either Lumber or plywood. In a given week the mill can turn out 400 units of production, of which 100 units of lumber and 150 units of plywood are required by regular customers. The profit on a unit of lumber is $20 and on a unit of plywood is $30. How many units of each type should the mill produce in order to maximize profit.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Lumber Company can convert logs into either Lumber or plywood. In a given week the mill can turn out 400 units of production,
of which 100 units of lumber and 150 units of plywood are required by regular customers. The profit on a unit of lumber is $20 and
on a unit of plywood is $30. How many units of each type should the mill produce in order to maximize profit.
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As I understand this LINEAR PROGRAMMING problem, there are two obvious restrictions:
x >= 100 and y >= 150,
where x is the (unknown) number of units of lumber and y is the unknown number of units of plywood.
The next restriction is
x + y <= 400 - (100+150), or x + y <= 150.
The objective function is z = 20x + 30y, which you must maximize.
The setup is done.
The rest is just arithmetic, if you know what the LINEAR PROGRAMMING METHOD is.
You can look into this link
https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1058105.html
https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1058105.html
I solved there another problem, but you can still understand the idea of the LINEAR PROGRAMMING METHOD from there,
or refresh your knowledge.
Good luck !
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