Posted by **May Ann Pascual Aragon** on Friday, March 22, 2013 at 10:11am.

Mark found out that his profit varies as the product of the amount spent for production and the square root of the amount spent for advertising. If his total available budget for these expenses is P1.5 million, how should he allocate his funds to maximize his profits

- Math -
**Steve**, Friday, March 22, 2013 at 10:43am
If p is spent on production, and a on advertising, and the total budget is n,

P = kp√a

p+a <= n, so p = n-a

P = k(n-a)^2 √a

dP/da = -2k(n-a)√a + k(n-a)^2/(2√a)

= k(n-a)(n-5a)/(2√a)

So, maximum profit occurs when 1/5 of the budget is allocated to advertising

## Answer This Question

## Related Questions

- Math( help please ! ) - The profit p(x) of a cosmetics company , in thousands of...
- Math( help please ! ) - The profit p(x) of a cosmetics company , in thousands of...
- Math - The profit p(x) of a perfume company , in thousands of dollars,is given ...
- math - The profit p(x) of a cosmetics company in thousands of dollars is given ...
- math - Designer Dolls, Inc. found that the number N of dolls sold varies ...
- Math - Designer Dolls, Inc. found that the number of dolls sold, N, varies ...
- Algebra 2 - Designer Dolls, Inc. found that the number N of dolls sold varies ...
- Calculus - The relationship between the amount of money x that Cannon Precision ...
- Math-Help - A manufacturer has determined that pro t P (in dollars) is a ...
- Statistics - A household appliance manufacturer wants to analyze the ...

More Related Questions