Afirm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where Cla) R() is called the break-even point. Assume that the below table can be expressed as a linear
function
Find (a) the cost function (b) the revenue function, and (c) the profit function
(d) Find the break-even point and decide whether the product should be produced, given the restrictions on sales.
Fixed cost Variable cost Price of item
$750 $10 $35
According to the restriction, no more than 20 units can be sold
(a) The cost function is CK-
(Simplify your answer)
(b) The revenue function is -
(Simplify your answer)
(c) The profit function is -
(Simplify your answer)
(d) Select the correct choice below and to in the answer box within your choice
(Type a whole number)
OA The break-even point is units. Thus, the product should not be produced, given the restriction on sales.
OB. The break-even point is units. Thus, the product should be produced, given the restriction on sales.

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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