SOLUTION: 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

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(52804) (Show Source): You can put this solution on YOUR website!
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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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