At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
P= price x= attendance
x = kP +c for constants k and c
when P=12, x= 19000
when P= 9 , x= 26000
now you can form two eqns, solve for the constants c and k
19000 =12k +c 26000= 9k +c subtract the first from the second 7000= -3k --> k = -7000/3
sub that into one of the other eqns say the first , so c= 19000-12k = 47000
thats what ive done so far but nothing from there is making sense. I also have to describe what im doing in words so i prove i understand it.
so x= (-7000/3) P +47000
revenue = R = attendance times cost price
so R = P [ (-7000/3)P +47000 ] differentiate with respect to P , we want to maximise R while varying P
R = (-7000/3) P^2 + 47000P dR/dP = (-14000/3)P +47000 =0 for min/max
P = 3
now check, second derivative is d^2R/dP^2 = (-14000/3) which is less than zero , so we do get a maximum . so ticket price = $3 maximises revenue
wit its wrong
should be P = (-47000) / ( -14000/3 ) = $10.07 , that maximises revenue
$10.07 is the right answer. I still however have no idea how you got it. We haven't went over any problems by differentiating. I have no idea what that is.
well , this can be done by other methods , I am assuming you have done quadratic equations before , ie , you know how to find the vertex of a parabola?
and you know that the vertex ( which is a maximum or a minimum ) occurs on the axis of symmetry , and axis of symmetry of y= ax^2 +bx +c is x=-b / (2a)
yes that's what we're doing now
how did I know ;)
so if you go back to this eqn R = (-7000/3) P^2 + 47000P and find the axis of symmetry , which is P = -b/ (2a) , this will give you the x coordinate of the maximum point
which is 10.07, the answer
Ok i know how you got this answer but why is there no c in the ax^2+bx+c equation? and how did you get 2 P's in the equation R= (-7000/3)P^2 +47000P ?
"why is there no c? " , there just isnt "where did the two Ps come from" , look at how revenue was calculated, revenue = price x number of people