Question 1058509: 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? $
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
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? $
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.
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 !
|
|
|
