SOLUTION: Hello, I am having trouble understanding and solving this problem: A furniture company makes desks and cairs. A carpenter can make a chair in 5 hours and a desk in 8 hours. Fini

Algebra ->  Equations -> SOLUTION: Hello, I am having trouble understanding and solving this problem: A furniture company makes desks and cairs. A carpenter can make a chair in 5 hours and a desk in 8 hours. Fini      Log On


   

Question 984090: Hello, I am having trouble understanding and solving this problem:
A furniture company makes desks and cairs. A carpenter can make a chair in 5 hours and a desk in 8 hours. Finishers take 2.5 hours to paint a chair and 2 hours to paint a desk. The carpentry department has enough people to work up to 400 hours per week, and the finishing department can put 120 hours per week.
(a.) Write a system of inequalities to model the situation.
(b.) Graph the system to show the possible numbers of desks and chairs the company can produce in a week.
-Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= number of chairs made
y= number of desks made
5x%2B8y= time (hours) required for a carpenter to make x chairs and y desks.
So, highlight%285x%2B8y%3C=400%29 , because the carpentry department has enough people to work up to 400 hours per week.
2.5x%2B2y= time (hours) required for a finisher to paint x chairs and y desks.
So, highlight%282.5x%2B2y%3C=120%29 , because the finishing department can put 120 hours per week.
(a.) The system of inequalities to model the situation is
highlight%28system%285x%2B8y%3C=400%2C2.5x%2B2y%3C=120%29%29
(b.) The graph for the system is shown below.
The solution is the quadrilateral shaded.