anonymous
  • anonymous
The SneakerRama Company makes and sells sneakers. They have one linear function that represents the cost of producing sneakers and another linear function that models how much income they get from those sneakers. Describe the key features that would determine if these linear functions ever intercepted.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@Michele_Laino @mathstudent55 @mathmate
Michele_Laino
  • Michele_Laino
any linear function can be described by this formula: \[y = kx + h\] where k and h are coefficients, and x, and y are two variables
Michele_Laino
  • Michele_Laino
now, in your first case y is the cost of producing sneakers and for second linear function y is the income for sneakers

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Michele_Laino
  • Michele_Laino
what can be x?
anonymous
  • anonymous
um..the sneakers?
Michele_Laino
  • Michele_Laino
yes! the number of sneakers
anonymous
  • anonymous
Yay:) Now what?
Michele_Laino
  • Michele_Laino
we have to consider one functionat a time. So for first function if x=0, we have: y=h, namely if we have not produced sneakers then the cost is h
anonymous
  • anonymous
Ok, i see
anonymous
  • anonymous
so what would be the key features to determine if they intersected?
Michele_Laino
  • Michele_Laino
I rewrite the two functions as below: \[\begin{gathered} f\left( x \right) = {a_1}x + {b_1} \hfill \\ g\left( x \right) = {a_2}x + {b_2} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
we have intersection if: \[\begin{gathered} f\left( x \right) = g\left( x \right) \hfill \\ {a_1}x + {b_1} = {a_2}x + {b_2} \hfill \\ \left( {{a_1} - {a_2}} \right)x = {b_2} - {b_1} \hfill \\ \end{gathered} \]
anonymous
  • anonymous
alright, but how would I type that in word form?
Michele_Laino
  • Michele_Laino
and we have no solutions, if and only if: \[\large {a_1} - {a_2} = 0,\;{b_2} - {b_1} \ne 0\]
Michele_Laino
  • Michele_Laino
namely, if the producing rate is equal to the earning rate and the cost for producing no sneakers is different from the earning for no sneakers sold, then we have no intersection
anonymous
  • anonymous
ok but we have to determine the key features if they ever intersceted?
anonymous
  • anonymous
"Describe the key features that would determine if these linear functions ever intercepted." See?
Michele_Laino
  • Michele_Laino
yes!
anonymous
  • anonymous
so what would be the answer?
anonymous
  • anonymous
Can I ask another question please?
Michele_Laino
  • Michele_Laino
I think that the requested key can be this: the producing rate has to be different from the earning rate
anonymous
  • anonymous
OK:)
Michele_Laino
  • Michele_Laino
:)
anonymous
  • anonymous
Your boss hands you the monthly data that show the number of orders coming in to and out of the warehouse. The data are in the table below. Explain to your boss, in complete sentences, the solution to this system and what the solution represents. Month No. of orders in No. of orders out January (1) 3 3 February (2) 6 4 March (3) 9 5 April (4) 12 6
anonymous
  • anonymous
# of orders in: 3 6 9 12
anonymous
  • anonymous
#of orders out: 3 4 5 6
Michele_Laino
  • Michele_Laino
we can write the relationship between the orders out y, as a function of the orders in x, like below: \[\Large y = \left( {x - 1} \right) + 3\]
anonymous
  • anonymous
ok:)
Michele_Laino
  • Michele_Laino
please wait
anonymous
  • anonymous
Alright:P)
Michele_Laino
  • Michele_Laino
no, I my formula is wrong
Michele_Laino
  • Michele_Laino
my fromula is wrong
anonymous
  • anonymous
that's okay:)
anonymous
  • anonymous
we can always start over
Michele_Laino
  • Michele_Laino
we have two linear equations. Namely the relationship between months x and orders out f(x), which is: \[\Large f\left( x \right) = \left( {x - 1} \right) + 3\]
Michele_Laino
  • Michele_Laino
the second relationship is between the months x and the orders in g(x): \[\Large g\left( x \right) = 3x\]
anonymous
  • anonymous
ok:) I see
Michele_Laino
  • Michele_Laino
the solution of your system is given solving this equation: \[\Large \begin{gathered} f\left( x \right) = g\left( x \right) \hfill \\ \\ \left( {x - 1} \right) + 3 = 3x \hfill \\ \end{gathered} \] solve please, for x
anonymous
  • anonymous
ux x- I got x+2=3x, then I got 2x+2
Michele_Laino
  • Michele_Laino
I got: 2x=2
Michele_Laino
  • Michele_Laino
so, x=?
anonymous
  • anonymous
1
Michele_Laino
  • Michele_Laino
that's right!
Michele_Laino
  • Michele_Laino
it means that at first month the orders in are equal to the orders out
Michele_Laino
  • Michele_Laino
more precisely: the number of orders in is equal to the number of orders out
anonymous
  • anonymous
Thanks! S :P)

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