SOLUTION: 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 h

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(52908) (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.

RELATED QUESTIONS
Please I have put this question up several times and no one has given me an answer. A... (answered by ankor@dixie-net.com)

A manufacturer produces two models of the same toy: Model A and Model B. Model A takes 4... (answered by ankor@dixie-net.com)

A manufacturer produces two models of the same toy; Model A and Model B. Model A takes 4 (answered by mananth)

A telephone company manufactures two diffrent models of phones: Model 120 is cordless and (answered by Theo)

How do I set this problem up to solve and check? A company produces 2 model bikes; Model (answered by Theo)

A small company produces both standard and deluxe playhouses. The standard playhouse... (answered by stanbon)

A manufacturer produces three models of bicycles. The time (in hours) required for... (answered by ikleyn)

A manufacturer produces two models of bicycles. TO produce one bike of model A, it takes (answered by Theo)

A small company produces both standard and deluxe playhouses. The standard playhouses... (answered by ankor@dixie-net.com)