How many television sets of each model should be produced so that the company makes use of all the available labor time?

Question

create a system of linear equations in two variables that models this situtation using the graphying or elemination method 

 

A company makes televisions manufacutres two models, Model X and Model Y. The company is able to make a total of 25 Tv's per week. They have 9 employees who can make the TV's, and since each employees works 8 hours per day and 5 days a week, they have 360 hours of labor per week available. It requires 12 hours of labor to produce one model X television, and it takes 18 hours of labor to produce one model Y television. How many television sets of each model should be produced so that the company makes use of all the available labor time?

Answer 1

You have two equations from this:

Since you can make a total of 25 televisons -

 

1)  x + y = 25

For the labor time totaling to 360 hours we have

2) 12x + 18y = 360

 

We can solve for one variable in terms of the other

in equation 1 and then substitute that into equation 2.

 

x = 25-y    from equation 1.

 

12(25-y) + 18y = 360

300 - 12y + 18y = 360

300 + 6y = 360

6y = 60

y = 10

 

Since x+y = 25

         x+10=25

         x=15