blets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?

Question

The demand function for a tablet is given by the model p = 200 - 16x² where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?

Answer 1

P=r-c= px-c =200x-16x^3 -50x = 150x -16x^3

is an odd function where f(x)=-f(-x)

f(2.5)=125= 150(2.5)- 16(2.5)^3= 375 - 250 =125

= -f(-2.5)=-(-375+250)=125

x=.91506351 million is the other positive solution to

16x^3 -150x +125=0

x= about 915,064 tablets has same $125 million profit

3rd x solution is <0