A division of Carter Enterprises produces "Personal Income Tax" diaries. Each diary sells for $8. The monthly fixed costs incurred by the division are $25,000, and the variable cost of producing each diary is $3.
A. What should be the level of sales in order for the division to realize a 15% profit over the cost of making the diaries?
2007-07-20 19:07:43 · 5 answers · asked by ehsan 2 in Science & Mathematics ➔ Mathematics
LOLOL
8x = (25000 + 3x) * 1.15
8x = 28750 + 3.45x
(8 - 3.45) x = 28750
4.55 x = 28750
x = 28750 / 4.55 = 6318.7
sooo ...
if you made 6319 diaries and sold theem , you would make 15% profit
/**********/
check:
cost:
= 6319 * 3 + 25000
= 18957+ 25000
= 43957
revenue
= 6319 * 8
= 50552
profit = revenue - cost
= 50552 - 43957
= 6595
%proofit =100 *profit/cost = 100* 6595 / 43957 = 15.0032% ...
2007-07-20 19:11:48 · answer #1 · answered by atheistforthebirthofjesus 6 · 0⤊ 1⤋
Let N be the number of diaries made and sold (it is assumed that they make only that number of diaries as they can sell).
N x 8 = (25000 + N x 3) x 1.15 (that is fitfteen percent profit)
8N = 28750 + 3.45N
(8 - 3.45) N = 28750
4.55 N = 28750
N = 6318.68...
Since N cannot be other than an integer we can take that as 6319.
2007-07-21 02:23:54 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
. That's easy. Kind of work backward and put every little detail down on paper, like a 'paper trail'.
15% profit on $25K = $3.75K. The profit on each diary is 8-3 + $5. So 3,750 / 5 = 750. Ya need to sell 750 diaries to get a profit of $3.75K. .
2007-07-21 02:18:01 · answer #3 · answered by jim bo 6 · 0⤊ 2⤋
5750 books sold would put you at %15 profit including the $3 variable cost.
2007-07-21 02:24:32 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Revenue, R=8n
Costs, C=3n+25000
Profit, P = R-C = 5n-25000
for 15% profit,
P-C = 0.15 C **** mistake here
Should be
R-C= 0.15C
P=0.15C
5n -25000 = 0.15 x (3n +25000)
5n -25000 = 0.45 n + 3750
4.55n = 28750
n=6318.7
ie 6319
2007-07-21 02:14:09 · answer #5 · answered by Anonymous · 0⤊ 0⤋