A computer rework center has the capacity to rework 300 computers per day. The expected number of computers needing to be reworked per day is 225. The center is paid $26 for each computer reworked. The fixed cost of renting the reworking equipment is $250 per day. Work space rents for $150 per day. The cost of material is $18 per computer and labor costs $3 per computer. What is the break-even number of computers reworked per day?
Answers
Answer:
The number of computers that must be repaired each day to break even is 80.
Step-by-step explanation:
Step : 1 80 computers must be reworked per day to break even.
Detailed explanation:
The number of computers needed to reach break-even each day is the number of computers needed to bring total income and total expenses into balance.
Step : 2 Let y be the daily break-even number of reworked computers.
Each repaired PC brought about $26 in revenue.
$26y is the total income for the reworked computers.
Rental fees for the reworking equipment are fixed at $250 per day.
Daily office rental is $150.
Materials cost per computer is $18.
Materials cost for y computers is y $18 = $18y.
$3 is the labour cost per computer.
$3y is the labour cost for y computers.
Step : 3 Total expenditure = $250 + $150 + $18y + $3y = $400 + $21y
Total revenue = total expenditure
$26y = $400 + $21y
$26y - $21y = $400
$5y = $400
y = $400/$5 = 80.
Step : 4 Fixed costs equal the break-even threshold (selling price per unit –variable costs per unit)
This formula will be used to determine the break-even point, or the number of computers that must be rebuilt for the business to break even and make no profit.
Step : 5 Replace the aforementioned values with:
Break-even point is calculated as ($150 per day plus $250 per day) / ($26 per unit - ($18 per unit plus $3 per unit)
$400 per day / $5 is the break-even threshold.
Breakeven point equals 80 units daily.
To cover all daily costs, the corporation has to rebuild 80 PCs.
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80 computers are reworked each day to reach break-even.
Given:
Fixed rental fees for reworking equipment per day = $250
Workspace rent per day = $150
Cost of material per computer = $18
Labor cost per computer = $3
Expected rework computer per day = 225
Revenue per computer = $26
We must figure out how many computers must be reworked in order for the total revenue to equal the total cost before we can calculate the break-even number of computers per day.
Total Revenue = ((Number of Reworked Computers) × (Revenue per computer reworked)
Total cost = Fixed cost of renting equipment + Workspace rent + (Materials + Labor per computer) × (Number of computers reworked)
Let N be the break-even number of computers reworked per day.
Let's enter the specified values:
Total Revenue = ($26) × N
Total cost =$250 + $150 + ($18 + $3) × N
Since 225 computers are anticipated to require rework each day, we can set the two equations equal to one another to determine the number of computers needed to break even:
$26N = $400 + 21N
$26N - $21N = $400
$5N = $400
N = = $80.
As a result, this indicates that the facility will break even and start making a profit if it reworks 80 or more computers per day.
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