Answer
a) Their revenues are respectively 408, 468 and 432 dollars
b) 468.75 dollars
Work Step by Step
a) Let's find R(4), R(6) and R(8)
R(4), p is now 4
= -12*4*4 + 150*4
=-12*16 + 600
= -192 + 600
=408
R(6), p is now 6
=-12*6*6 + 150*6
=-12*36 + 900
=-432 + 900
=468
R(8), p is now 8
=-12*8*8 + 150*8
=-12*64 + 1200
=-768 + 1200
= 432
So, their revenues are respectively 408, 468 and 432 dollars
b) The function R(p)= -12p*p + 150p has a maximum of x=-b/2a because a<0. Calculate the price charged per animal to yield a maximum revenue.
Let's say that a=12 and b=150
x= -b/2a
x=-150/2(-12)
x= 150/24
x=6.25
Now, we input this into the function to calculate the revenue.
R(p)= -12p*p + 150p
R(6.25)= -12*6.25*6.25 + 150*6.25
R(6.25)= -12*39.0625 + 937.50
R(6.25)= -468.75 + 937.50
R(6.25)= 468.75
468.75 dollars
