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 vloraboy February 21st, 2009 10:54 AM

Can somebody help solve this problems please

A radio manufacturing firm has fixed cost of \$25.000 cost and variable cost of \$75.80 per radio. The radio sells for \$119.95. Write an expression for the profit function and find the number of radios that must be sold to break even. If money is invested at 9%, what is the effective annual rate if the investment is compounded a) quarterly? b) monthly? c) daily? d) countinuously?  skipjack February 26th, 2009 01:16 AM Why are there three zeros in the fixed cost? Is it typed correctly? For the questions about interest rates, read this article.  shynthriir February 26th, 2009 09:11 AM Re: CAN SOMEBODY HELP SOLVE THIS PROBLEMS PLEASE If the zeros are correct and the fixed cost is just \$25.00, then you break even after the first radio because 119.95 - 25.000 - 75.80 = 19.15. Meaning you are making \$19.15 profit off the first radio sold. Now, assuming the fixed cost is supposed to be \$250.00, the formula becomes
$119.95x= 250 + 75.8x$

$44.15x= 250$

$x= 5.66$

Because you can't sell .66 of a radio, round up to the nearest digit. So you need to sell 6 radios to start turning a profit. Total profit can be calculated with the function

$f(x)= 44.15x - 250$

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As for the second question, I could be wrong, but here it goes:

Quarterly:$1 - (1 + \frac{0.09}{4})^4= 9.31%$

Monthly:$1 - (1 + \frac{0.09}{12})^{12}= 9.38%$

Daily: $1 - (1 + \frac{0.09}{365})^{365}= 9.42%$

Countinuously: not sure how to do this one though
You could do it with calculus though like

$\lim_{x \to \infty} 1 - (1 + \frac{0.09}{x})^x$

The limit should also equal $\infty$ I believe, again, don't quote me on it though...

 skipjack April 2nd, 2009 01:05 PM

That limit is 1-e^0.09, but is the formula correct?

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