Problema Solution
Did you mean: the total cost function for producing product is c ( x ) = 100 x ^6 + 1300x +1000 where x equals the number of units produced in thousands and c( x) equals total cost ( in thousands ) of dollars .) . Each unit of product sells $ 2000. using x as defined above . formulate tht total revenue function and determine
a ) the level of production required to break - even .
b )the level of output that would result in maximum profit .
c ) the expected maximum profit ?
Answer provided by our tutors
the total revenue function is:
R(x) = 2000x
a ) the level of production required to break - even
R(x) = c(x)
2000x = 100x^6 + 1300x +1000
x^6 - 7x + 10 = 0
since x^6 - 7x + 10 is always greater than 0 break even will never happen
we can also conclude that by looking at the graph of the function: y = x^6 - 7x + 10
click here to see the graph:
this graph never intercept the x-axis.
b) the level of output that would result in maximum profit
P(x) = R(x) - c(x)
P(x) = x^6 - 7x + 10
we need to find such x so that the function y = x^6 - 7x + 10 has maximum
from the graph at a) we conclude that the function has no upper limit thus by increasing the output the profit grows as well
c ) the expected maximum profit
see a) and b)