Question 1171582: A small tool manufacturer produces a standard and cordless model power drill. The standard model takes 2 hours of labor to assemble and the cordless model 3 hours. There are 72 hours of labor available per week for the drills. Material costs for the standard drill are $10, and for the cordless drill they are $20. To maximize profits, the company wished to limit material costs to $420 each week. How many of the cordless drills should be produced to use all of the available resources?
Let y = cordless drills
Answer by ikleyn(52887)   (Show Source):
You can put this solution on YOUR website! .
A small tool manufacturer produces a standard and cordless model power drill.
The standard model takes 2 hours of labor to assemble and the cordless model 3 hours.
There are 72 hours of labor available per week for the drills.
Material costs for the standard drill are $10, and for the cordless drill they are $20.
To maximize profits, the company wished to limit material costs to $420 each week.
How many of the cordless drills should be produced to use all of the available resources?
~~~~~~~~~~~~~~~~
Let x be the number of standard models produced each week, and let y be the number of cordless models produced.
Then you have these equations (assuming us all resources)
2x + 3y = 72 (1) (labor hours) and
10x + 20y = 420 (2) (material cost)
or, equivalently,
2x + 3y = 72 (1')
x + 2y = 42 (2')
To solve it, multiply equation (2') by 2 (both sides). You will get
2x + 3y = 72 (1'')
2x + 4y = 84 (2'')
Now subtract equation (1'') from equation (2''). You will get
4y - 3y = 84 - 72 = 12.
Thus, the unknown "y" is just found: y = 12.
To find "x", substitute the value y= 12 into equation (1). You will get
2x + 3*12 = 72
2x = 72 - 36 = 36
x = 18.
ANSWER. 18 standard models and 12 cordless models.
Solved.
Do not forget to post your "THANKS" to me for my teaching.
|
|
|
