A one-product company finds that its profit, P in millions of dollars, is given

Question

A one-product company finds that its profit, P in millions of dollars, is given by the following equation where a is the amount on advertising in million of dollars, and p is the price charged per item of the product in dollars:

P(a,p)= 4app+50p-9p^2-1/10a^2p-120

Find the maximum value of P and the values of a and p at which it is attained.

A) The maximum of P is attained when a is $____ million and p is $___


B)The maximum value of P is $___ Million

What is the answer for A and what is the answer for B in millions? Please

Explanation / Answer

Pa = 4pp - 1(-2)a-3/(10p) = 0

==> 4ppa3 + 2/10p =0

==> 4p3a3 = -1/5

==>(ap)3 = -1/20

Pp = 8ap + 50 -18p -(1/10a2)(-1/p2) = 0

==> 8 (ap)3 + 50 (ap)2 - 18 p(ap)2 = 1/10

==> -8/20 + 50(0.1357) - 18(-1/20)/a = 1/10

==> 6.285 = -18/20a

==> a = -0.1432

for a = -0.1432

==> ap = -0.3684 ==> p = 2.5726

for (-0.1432,2.5726)

P = -3.7909 + 128.63 - 59.5644 -1.8955 -120

= -52.9094

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