Question 1058509
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A manufacturer produces two models of mountain bikes. Model A requires 5 hours of assembly time and 2 hours of painting time, 
and Model B requires 4 hours of assembly time and 3 hours of painting time. The maximum total weekly hours available in 
the assembly department and the painting department are 200 hours and 108 hours, respectively. 
The profits per unit are $25 for Model A and $15 for Model B. How many of each type should be produced to maximize profit?


 bikes of Model A


 bikes of Model B

What is the maximum profit? $
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<pre>
Let x = # model A bikes to produce,
    y = # model B bikes to produce.

Then the restrictions are

5x + 4y <= 200,     (assembly time)
2x + 3y <= 108.     (painting time)

Two other obvious restrictions are x >= 0  and  y >= 0.

The objective function is z = 25x + 15y, which you must to maximize. 

The setup is done. 
The rest is just arithmetic, if you know what the LINEAR PROGRAMMING METHOD is.
</pre>

You can look into this link

<A HREF=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</A>


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 !