Maximizing Profit: Solving Polynomial for MP3 Player Ad Expenses

In summary, the conversation is about finding the smaller of two ad amounts that will yield a profit of $2,500,000 for a particular MP3 player. The equation given is P = -76x^3 + 4830x^2 - 320000, with x representing ad expense in tens of thousands of dollars. Attempts to solve the problem through factoring or dividing by possible zeros have been unsuccessful, and the best solution is to use an approximate answer through a graphing calculator.
  • #1
Bo_
9
0

Homework Statement



P is profit in dollars of a particular mp3 player.

P = -76x^3 + 4830x^2 - 320000, 0 < x < 60

x is ad expense (in tens of thousands of $.) Find the smaller of two ad amounts that yield a profit of $2,500,000.



The attempt at a solution

All I can do is get this:

-76x^3 + 4830x^2 - 2,820,000 = 0

Now what do I do? I can't seem to factor. The only other way I know of is dividing by possible zeros, and I'm not feeling good about looking for the factors of 2.82 million.
 
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  • #2
I'm pretty sure it doesn't factor. Are you sure you aren't just supposed to give an approximate answer?
 
  • #3
I don't know but that'll have to do. There doesn't seem to be another way.
 
  • #4
-boo boo-
sorry.
 
Last edited:
  • #5
Dick said:
In what way does this contribute to helping the OP solve the problem on his own?

Oh my apologies...

*removes post*.
 
  • #6
matadorqk said:
Oh my apologies...

*removes post*.

Thanks. You do get my point, right? I'm not trying to criticize your wish to help.
 
Last edited:
  • #7
Yea, the best I can think of is the approximate answer as well.

I just used a brute method on my calculator to narrow it down. You may want to use a graphing calculator(available online) to see what the graph looks like at least.
 

1. How do you determine the polynomial equation for maximizing profit for an MP3 player ad campaign?

The polynomial equation for maximizing profit can be determined by considering the cost of producing and promoting the MP3 player, the price at which it will be sold, and the expected demand for the product. This equation can be derived using principles of algebra and calculus.

2. How do you find the maximum profit using the polynomial equation?

To find the maximum profit, we can use the first derivative of the polynomial equation to determine the critical point. This will give us the value of the independent variable at which the profit is maximized. We can then substitute this value back into the original equation to find the maximum profit.

3. Can the polynomial equation be used for any type of product or service?

Yes, the polynomial equation for maximizing profit can be applied to any product or service as long as all the relevant variables are taken into consideration. However, the specific coefficients and variables in the equation may vary depending on the specific product or service being analyzed.

4. How can this equation be used to make strategic decisions for the MP3 player ad campaign?

Once the polynomial equation has been derived and the maximum profit has been determined, it can be used to make strategic decisions for the ad campaign. For example, the equation can be used to determine the optimal price point, advertising budget, and production volume that will result in the highest profit for the company.

5. Are there any limitations to using a polynomial equation for maximizing profit?

While a polynomial equation can be a powerful tool for maximizing profit, it is important to note that it is still a simplified model of real-world scenarios. It may not accurately capture all the complexities and variables involved in a particular market or industry. Therefore, it is important to use the equation as a guide and to also consider other factors and data when making important business decisions.

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