Question 1026583: Quickprint services operates several franchises where it prints brochures, business cards and stationery. it plans to sell 80 jobs next week at an average cost of $52 each. its weekly expenses are $1840.
a) How much must Quickprint charge for each job to break even?
b)if it wishes to make a profit of $1200, what price does it have to charge?
c) if it sells 90 jobs at the price determined in part b, how much profit will be realized?
d) if Quickprint sells 100 jobs through a special promotion, what is the minimum price it could charge to break even?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if i understand this problem correctly, this is what happens.
it plans to sell 80 jobs next week at an average cost of 52 dollars each.
its fixed weekly expenses are 1840.
it's total cost for the week is therefore equal to 1840 + 80 * 52 = 6000 dollars.
profit is equal to revenue minus cost.
profit is equal to 0
cost is equal to 6000.
solve for revenue to get revenue is equal to 6000.
since revenue is equal to the number of projects * revenue per project, then if we let x equal to the revenue per project, we get:
6000 = 80 * x
solve for x to get x = 6000 / 80 = 75 dollars per project.
they need to charge 75 dollars per project to break even.
profit = revenue minus cost.
revenue = 80 * 75 = 6000
cost = 1840 + 80 * 52 = 1840 + 4160 = 6000
profit = revenue minus cost becomes profit = 6000 - 6000 = 0.
that's the breakeven point.
if they want to make 1200 profit, then the equation of profit = revenue minus cost becomes:
1200 = revenue minus cost.
cost is the same at 6000.
equation becomes 1200 = revenue minus 6000.
revenue is equal to 80 * x, where x represents the revenue per project.
equation becomes 1200 = 80 * x - 6000
add 6000 to both sides to get 7200 = 80 * x
solve for x to get x = 7200 / 80 = 90.
they need to charge 90 dollars per project to get a profit of 1200.
profit = revenue - cost.
revenue = 80 * 90 = 7200
cost = 1840 + 80 * 52 = 6000
profit = 7200 - 6000 = 1200.
if they sell 90 jobs at 90 dollars a job, then you get:
profit = revenue minus cost.
revenue = 90 * 90 = 8100.
cost = 1840 + 90 * 52 = 6520.
you get profit = 8100 - 6520 = 1580.
if they sell 90 jobs at 90 dollars a job, their profit is 1580.
if they want to sell 100 jobs through a special promotion, and they want to break even, then the formula of profit = revenue - cost becomes:
revenue = 100 * x
x represents the revenue per job.
cost = 1840 + 100 * 52 = 7040.
profit = 0.
profit = revenue - cost equation becomes:
0 = 100 * x - 7040
solve for x to get x = 7040 / 100 = 70.4 dollars per project.
they would need to charge $70.40 per project to break even.
revenue is 70.4 * 100 = 7040.
cost = 1840 + 100 * 52 = 7040.
profit = revenue minus cost becomes profit = 7040 - 7040 = 0.
those are your solutions.
in summary, the solutions are:
a) How much must Quickprint charge for each job to break even?
they need to charge 75 dollars per project.
b)if it wishes to make a profit of $1200, what price does it have to charge?
they need to charge 90 dollars per project.
c) if it sells 90 jobs at the price determined in part b, how much profit will be realized?
their profit will be 1,580 dollars.
d) if Quickprint sells 100 jobs through a special promotion, what is the minimum price it could charge to break even?
they need to charge 70.40 dollars per project.
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