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Question 1155260: A manufacturing firm has 120 hours per week available in one of its department. Two products are produced through this department.
Product A requires 4 hours per unit and product B requires 6 hours per unit in this department.
If x equals the number of units of product A per week and y equals the number of units of products B produced per week.
a) Determine the equation which states the total time expended for producing these two products equals 120 hours per week
b) Rewrite the equation in the slope intercept from and identify the slope and y intercept
c) Interpret the meaning of the slope and y intercept in this application.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of units of product A per week.
y = number of units of product B per week.
product A requires 4 hours per unit and product B requires 6 hours per unit.
total hours available per week = 120.
equation becomes 4x + 6y = 120
convert this to slope intercept form as follows:
subtract 4x from both sides of the equation and arrange the right side of the equation in descending order of degree to get:
6y = -4x + 120
divide both sides of this equation by 6 to get:
y = -4/6 * x + 120 / 6
simplify to get:
y = -2/3 * x + 20
questions to answer are:
a) Determine the equation which states the total time expended for producing these two products equals 120 hours per week
4x + 6y = 120
this equation says that 4 hours are expended for every unit of product A and 6 hours are expended for every unit of product B.
x = the number of units for product A.
y = the number of units for product B.
b) Rewrite the equation in the slope intercept from and identify the slope and y intercept
y = -2/3 * x + 20
the general form of the slope intercept form of the equation is y = mx + b
m is the slope and b is the y-intercept.
m = -2/3
y-intercept = 20
c) Interpret the meaning of the slope and y intercept in this application.
the y-intercept is the value of y when x = 0.
when x = 0, the formula becomes y = 20.
this is saying that, if no units of product A are produced, and 120 hours a week are still required, than 20 units of product B are produced.
the slope tells you the change in the number of units of y for every change in the number of units for x.
a slope of -2/3 is equivalent to (-2/3) / 1.
this says that, when x increases by 1, y decreases by 2/3.
this translates to the change in the number of units of product B for every change in the number of units of product A.
it says that, when the number of units of product A increases by 1, the number of units of product B decreases by 2/3.
it might be useful to show you what happens via a graph.
the graph is shown below.
you can see that, when x = 0, y = 20.
this means that no units are produced for product A and 20 units are produced for product B.
you can see that, when x = 6, y = 16 and when x = 12, y = 12.
y = -2/3 * x + 20 is the equation.
when x = 6, y = -2/3 * 6 + 20 which becomes y = -4 + 20 which becomes y = 16.
when x = 12, y = -2/3 * 12 + 20 which becomes y = -8 + 20 which becomes y = 12.
the change in x from 6 to 12 is 6.
the change in y from 16 to 12 is -4.
the change in y divided by the change in x is -4/6 which simplifies to -2/3.
that's your slope.
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