Question

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.

Answer 1

Cost function, $C(x)=300+15x$

Revenue function, $R(x) = 30x$

Profit function, $P(x)=15x-300$

Break point $x=20$.

Fixed cost $=$ $$300$.

Variable cost $=$ $$15$.

Price of item $=$ $$30$.

Let $x$ be the number of items produced and sold.

a) Cost function $=$ Fixed cost $+$ variable cost \times number of items

So, $C(x)=300+15x$

b) Revenue $=$ Price of an item $\times$ number of items

So, $R(x) = 30x$

c) Profit $=$ Revenue $-$ Cost

$P(x)=R(x)-C(x)$

$P(x)=30x-300-15x$

$P(x)=15x-300$

d) Break even point $R(x)=C(x)$

$30x=300+15x$

$30x-15x=300$

$15x=300$

$x=20$.

So, the product should be produced for $20$ or more items.

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