Respuesta :
Answer:
The break-even point will be when he sold 220 items.
The cost of revenue when it sells the break-even number of products is $1210
Step-by-step explanation:
Cost of rent and utilities : $550
Average cost for 1 product to be manufactured : $3.00
Average price for a product sold in the store : $5.50
The break-even point occurs when the cost function equals the revenue function.
The equation for break even point (given):
[tex]550 + 3.00x = 5.50x[/tex]
where Let x represent the number of products sold.
So, to calculate the break even point i.e. x
[tex]550 = 5.50x - 3.00x [/tex]
[tex]550 = 2.50x [/tex]
[tex]\frac{550}{2.50} =x [/tex]
[tex]220=x [/tex]
So, the break-even point will be when he sold 220 items.
The cost of revenue when it sells the break-even number of products:
[tex] 5.50*220[/tex]
[tex]1210[/tex]
Hence The cost of revenue when it sells the break-even number of products is $1210
Using concepts of profit, revenue and cost, it is found that:
- The break-even point is x = 200.
- The cost or revenue when it sells the break-even number of products will be $1110.
Profit is revenue subtracted by cost, that is:
[tex]P(x) = R(x) - C(x)[/tex]
The costs are the fee plus the cost per item, thus:
[tex]C(x) = 500 + 3x[/tex].
The revenue is the earnings per each item sold, thus:
[tex]R(x) = 5.5x[/tex]
The break-even point is when the profit is 0, that is:
[tex]R(x) = C(x)[/tex]
Thus:
[tex]5.5x = 500 + 3x[/tex]
[tex]2.5x = 500[/tex]
[tex]x = \frac{500}{2.5}[/tex]
[tex]x = 200[/tex]
The break-even point is x = 200.
The cost or revenue are:
[tex]R(x) = 5.5x = 5.5(200) = 1110[/tex]
The cost or revenue when it sells the break-even number of products will be $1110.
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