Question

Al Sharqiyya is considering whether to pay $50,000 per year to lease a prisoner transfer facility in a prime location near Dammam. They estimate it will cost $50 per prisoner to process the paperwork at this new location. Al Sharqiyya is paid a $75 commission for each new prisoner they process.

What would be the Al Sharqiyya’s annual profit if they were to process 4,000 prisoners per year at this new location?

What is the breakeven point?

Answer 1

Given

Cost / year for prisoner transfer facility A = $50000

Processing cost / Prisioner B = $ 50

Processing Commision / Prisioner C = $ 75

No. of Prisioner they Process per year D = 4000

So

Annual Profit = ( C - B ) * D - A

Substituting the values, we get

Annual Profit = ($75 - $50) * 4000 - $50000

Annual Profit = $25 *4000 - $50000

Annual Profit = $100000 - $50000

Annual Profit = $ 50000

To find break even point --Basically we need to find "at what no. of Prisioners (Processing) their is neither profit nor loss"

So let X be the no. of prisioners processed per year

Annual Selling Value = C * X

Annual Cost Value = A + ( B * X )

At Break even

Annual Selling value = Annual Cost value

C*X = A + (B * X)

Substituting the values

$75 X = $50000 + ( $50 X)

$75 X - $25 X = $50000

$25 X = $50000

X = ($ 50000 / $25 )

X = 2000 ----This is the break even point

If they Process 2000 Prisioners then they have reached a break even point.

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