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Question 1183144: (Product Mix) A company produces two products. Weekly labor availability equals 150 labor-hours. Each unit
of product 1 requires 3 labor-hours and each unit of product 2 requires 4.5 labor-hours. If management wishes to
use all labor hours, the equation 3x + 4.5 y = 150 is a statement of this requirement, where x equals the number
of units produced of product 1 and y equals the number of units produced of product 2. Rewrite the equation in
slope-intercept form and interpret the meaning of the slope and y-intercept. Solve for the x intercept and
interpret its meaning.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation is 3x + 4.5y = 150
x represents the number of units of product 1 that are produced.
y represents the number of units of product 2 that are produced.
slope intercept form is y = mx + b
m is the slope
b is the y-intercept.
subtract 3x from both sides of the equation to get:
4.5y = 150 - 3x
divide both sides of the equation by 4.5 to get:
y = 150/4.5 - 3/4.5 * x
reorder the terms in descending order of degree to get:
y = -3/4.5 * x + 150/4.5
that's the equation in slope intercept form.
the graph of that equation is shown below:
the slope is the change in the value of y for the corresponding change in the value of x.
the equation in slope intercept form is y = -3/4.5 * x + 150/4.5.
since the slope is equal to -3/4.5, then every positive 4.5 change in the value of x will give you a negative change of 3 in the value of y.
this can be seen in the graph when x = 15.5 and x = 20
when x = 15.5, y = 23
when x = 20, y = 20
when x went up 4.5 units, y went down 3 units.
the y-intercept = 150/4.5
that's the value of y when the value of x = 0.
keep in mind that x represents the number of units produced for product 1 and y represents the number of units produced for product 2.
since 150 labor hours have to be used, then when x = 0, no labor hours are used for product 1 and 150 labor hours are used for product 2.
since each unit of product 2 requires 4.5 hours of labor, then 150/4.5 units of product 2 are produced while 0 units of product 1 are produced.
150/4.5 = 33.333 as shown on the graph for the coordinate point of (x,y) = (0,33.333)
the x-intercept = 50
that's the value of x when the value of y = 0.
keep in mind that y represents the number of units produced for product 2 and x represents the number of units produced for product 1.
since 150 labor hours have to be used, then when y = 0, no labor hours are used for product 2 and 150 labor hours are used for product 1.
since each unit of product 1 requires 3 hours of labor, then 150/3 units of product 1 are produced while 0 units of product 2 are produced.
150/3 = 50 as shown on the graph for the coordinate point of (x,y) = (50,0).
the y-intercept = (0,33.333) which means that 33.333 units of product 2 are produced when 0 units of product 1 are produced.
the x-intercept = (50,0) which means that 50 units of product 1 are produced when 0 units of product 2 are produced.
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