1.) Suppose the manufacturer of a clothes washer has found that, when the unit price is p dollars, the revenue R is R(p) = -4p2 + 4000p. What unit price should be established for the washer to maximize the revenue?

2.) The function R(x) = -0.0065x2 + 0.23x + 8.47 models the American marriage rate R (the number of marriages per 100 population) x years after 1960. Based on this function, in what year was the marriage rate the highest?

PLEASE HELP!!!!!! IT WOULD BE A LIFE SAVER !!

Question

1.) Suppose the manufacturer of a clothes washer has found that, when the unit price is p dollars, the revenue R is R(p) = -4p2 + 4000p.  What unit price should be established for the washer to maximize the revenue?



2.) The function R(x) = -0.0065x2 + 0.23x + 8.47 models the American marriage rate R (the number of marriages per 100 population) x years after 1960.  Based on this function, in what year was the marriage rate the highest?



PLEASE HELP!!!!!! IT WOULD BE A LIFE SAVER !!

paxpolaris · Answer

using derivatives??

anonymous · Answer

??

paxpolaris · Answer

have you learned any calculus...? 11-12th grade math

anonymous · Answer

no this is precalculus

paxpolaris · Answer

all right ...
do you know how to find the co-ordinates of the vertex of a quadratic function $$\Large f(x)=ax^2+bx+c$$

anonymous · Answer

yes

anonymous · Answer

b/2a

paxpolaris · Answer

it's NEGATIVE of that...
the vertex (max or min) of f(x) is at $\large x=-{b \over2a}$

that's all you need to use for both questions.

paxpolaris · Answer

$$1)\ \Large\ p=-{4000\over-4}=$1000.$$

2)$$\Large x=-{0.23 \over-0.0065}$$then add 1960... to get about 1995

anonymous · Answer

oh ok thank you that was easier thatn i thought