SOLUTION: Can someone help me with this problem please Back Packs, Inc., finds that the cost to make x back packs is C = 129x + 6687, while the revenue produced from them is R = 171x (C a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can someone help me with this problem please Back Packs, Inc., finds that the cost to make x back packs is C = 129x + 6687, while the revenue produced from them is R = 171x (C a      Log On


   

Question 161581: Can someone help me with this problem please
Back Packs, Inc., finds that the cost to make x back packs is C = 129x + 6687, while the revenue produced from them is R = 171x (C and R are in dollars). What is the smallest whole number of backpacks, x, that must be sold for the company to show a profit?
160
23
280,854 or
2,006,100
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When C+=+R, Cost equals Revenue, that is the break-even point. If
you sell 1 more backpack, you will show the smallest profit possible.
C+=+129x+%2B+6687
R+=+171x
C+=+R
129x+%2B+6687+=+171x
Subtract 129x from both sides
42x+=+6687
x+=+159 to the nearest whole number
Let Profit = P
P+=+R+-+C
I'll find the Profit for 158 backpacks, which should be negative
and for 160 backpacks which should be positive
P+=+171x+-+%28129x+%2B+6687%29
P+=+171x+-+129x+-+6687
P+=+42x+-+6687
P%5B1%5D+=+42%2A158+-+6687
P%5B1%5D+=+6636+-+6687
P%5B1%5D+=+-51
P%5B2%5D+=+42%2A160+-+6687
P%5B2%5D+=+6720+-+6687
P%5B2%5D+=+33
If 160 backpacks are sold, the profit will be $33, the smallest possible