SOLUTION: I am not sure what this word problem is asking, it needs to be solved using systems of linear equations. A manufacturer produces two modles of mountain bicycles.The times(in hou

Question 4797: I am not sure what this word problem is asking, it needs to be solved using systems of linear equations.
A manufacturer produces two modles of mountain bicycles.The times(in hours) required for assembling and painting are: Model A Model B
Assembling 5 4
Painting 2 3
The maximum total weekly hours available in the assembly department and the paint department are 200 hours and 108 hours, respectivley. 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?
Answer by Abbey(339) (Show Source): You can put this solution on YOUR website!
We can assume that maximum profits in this case will occur when there is no unused time in either department.
The assembly department has 200 hours available
and the paint department has 108 hours available
Let A = the number of Model A bicycles built
Let B = the number of Model B bicycles built
Assembly time:
5A+4B=200
Paint time:
2A+3B=108
We have two equations:
5A+4B=200 =
2A+3B=108 =
Multiply the first equation by -2 and the second by 5 to eliminate:
-10A+ -8B= -400
10A+ 15B= 540
Add them:
7B=140
Divide both sides by 7
B=20
Substitute back into the original equation:
2A+3(20)=108
2A+60=108
2A=48
A=24
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