Homework Help: Math

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

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