Respuesta :
Cost function, [tex]C(x)=300+15x[/tex]
Revenue function, [tex]R(x) = 30x[/tex]
Profit function, [tex]P(x)=15x-300[/tex]
Break point [tex]x=20[/tex].
Fixed cost [tex]=[/tex] $[tex]300[/tex].
Variable cost [tex]=[/tex] $[tex]15[/tex].
Price of item [tex]=[/tex] $[tex]30[/tex].
Let [tex]x[/tex] be the number of items produced and sold.
a) Cost function [tex]=[/tex] Fixed cost [tex]+[/tex] variable cost \times number of items
So, [tex]C(x)=300+15x[/tex]
b) Revenue [tex]=[/tex] Price of an item [tex]\times[/tex] number of items
So, [tex]R(x) = 30x[/tex]
c) Profit [tex]=[/tex] Revenue [tex]-[/tex] Cost
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=30x-300-15x[/tex]
[tex]P(x)=15x-300[/tex]
d) Break even point [tex]R(x)=C(x)[/tex]
[tex]30x=300+15x[/tex]
[tex]30x-15x=300[/tex]
[tex]15x=300[/tex]
[tex]x=20[/tex].
So, the product should be produced for [tex]20[/tex] or more items.
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