SOLUTION: A company produces two products. Weekly labour availability equals 200 labour hour. Each unit of product one require four labour hour and each unit of product to required 3.5 labou

Algebra ->  Linear-equations -> SOLUTION: A company produces two products. Weekly labour availability equals 200 labour hour. Each unit of product one require four labour hour and each unit of product to required 3.5 labou      Log On


   

Question 1198594: A company produces two products. Weekly labour availability equals 200 labour hour. Each unit of product one require four labour hour and each unit of product to required 3.5 labour hours. If management wishes to use all labour hours,then
1) make a linear equation using above data
2) read write the equation in slope intercept form
3) dantify the slope and y intercept
4) interpret the meaning of slope and y intercept
5) solve for the x intercept and interpret the meaning.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x represent the number of hours to make the first product.
let y represent the number of hours to make the second product.
the total hours available are 200.

the equation for total labor hours expended for each product is:
4x + 3.5y = 200.

that equation states.
4 hours for each unit of product 1 times x units plus 3.5 hours for each unit of product 2 times y units is equal to 200 hours total.

to convert that equation into slope intercept form, do the following:
start with 4x + 3.5y = 200
subtract 4x from from both sides of the equation to get:
3.5y = 200 - 4x
divide both sides of that equation by 3.5 to get:
y = 200/3.5 - 4/3.5 * x
arrange the equation in descending order of degree to get:
y = -4/3.5 * x + 200/3.5

the slope is -4/3.5
the y-intercept is 200/3.5

these two equations are equivalent.
the graph of both equations will generate the same straight line.
here's what it looks like.



the y-intercept is 200/3.5 = 57.14285714.
it is the value of y when the value of x is 0.
on the graph, it is shown at (0,57.143).
you can use either the standard form of the equation or the slope intercept form of the equation to solve for it.

the x-intercept is the value of x when y is equal to 0.
you can use either the standard form of the equation or the slope intercept form of the equation to solve for it.
using the standard form of 4x + 3.5y = 200, replace y with 0 to get 4x = 200, solve for x to get x = 50.
using the slope intercept form of y = -4/3.5 * x + 200/3.5, replace y with 0 to get 0 = -4/3.5 * x + 200/3.5
add 4/3.5 * x to both sides of the equation to get:
4/3.5 * x = 200/3.5
multiply both sides of this equation by 3.5 * x to get:
4 * x = 200
solve for x to get:
x = 200/4 = 50.
on the graph, it is shown as (50,0).