Math
posted by May Ann Pascual Aragon .
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
If p is spent on production, and a on advertising, and the total budget is n,
P = kp√a
p+a <= n, so p = na
P = k(na)^2 √a
dP/da = 2k(na)√a + k(na)^2/(2√a)
= k(na)(n5a)/(2√a)
So, maximum profit occurs when 1/5 of the budget is allocated to advertising
Respond to this Question
Similar Questions

Math( help please ! )
The profit p(x) of a cosmetics company , in thousands of dollars . is given by p(x) =5t^2=400x2550, where x is the amount spent on advertising in thousands of dollars a) determine the maximum profit the company can make b) dtermine … 
Math( help please ! )
The profit p(x) of a cosmetics company , in thousands of dollars,is given by p(x)=5x^2+400x2550, where x is the amount spent on advertising , in thousands of dollars a) determine the max profit the company can make b)Determine the … 
Math
The profit p(x) of a perfume company , in thousands of dollars,is given by p(x)=5x^2+400x2550, where x is the amount spent on advertising , in thousands of dollars a) determine the max profit the company can make b)Determine the … 
Calculus
The relationship between the amount of money x that Cannon Precision Instruments spends on advertising and the company's total sales S(x) is given by the following function where x is measured in thousands of dollars. S(x) = 0.002x3 … 
math
The profit p(x) of a cosmetics company in thousands of dollars is given by P(x) = 5x^2 + 400x  2550, where x is the amount spent on advertising, in thousands of dollars. What amount must be spent on advertising to obtain a profit … 
Statistics
A household appliance manufacturer wants to analyze the relationship between total sales and the company's three primary means of advertising (television, magazines, and radio). All values are in millions of dollars. They found the … 
math
Designer Dolls, Inc. found that the number N of dolls sold varies directly with their advertising budget A and inversely with the price P of each doll. The company sold 5200 dolls when $26,000 was spent on advertising and the price … 
Algebra 2
Designer Dolls, Inc. found that the number N of dolls sold varies directly with their advertising budget A and inversely with the price P of each doll. The company sold 1,800 dolls when $34,000.00 was spent on advertising, and the … 
Math
Designer Dolls, Inc. found that the number of dolls sold, N, varies directly as their advertising budget, A, and inversely as the price of each doll, P. Designer Dolls, Inc. sold 12,000 dolls when $50,000 was spent on advertising and … 
math
a company's monthly sales, in thousands, is given by s(x,y)=9x^.8y^.5. where x is the amount spent on newspaper advertising per month in thousands of dollars and y is the amount spent on radio advertising per month in thousands of …