The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even.
R(x) = 200 x -x squared; C(x) = 40x + 3375; 0 less than or equal to x less than or equal to 100

The manufacturer must produce ___ units to break even.

Question

contestada

Respuesta :

elcharly64 elcharly64 · Answer 1 · 2020-03-01T05:03:43+01:00

Answer:

The manufacturer should produce 25 units to break even

Step-by-step explanation:

Revenue and Cost Function

The revenue function R(x) is given as

[tex]R(x) = 200 x -x^2[/tex]

And the cost function is

[tex]C(x) = 40x + 3375[/tex]

Both valid in the range

[tex]0\leq x \leq 100[/tex]

We need to find the number of units that must be produced to break even, which means that the cost and revenue are the same:

[tex]R(x)=C(x)[/tex]

[tex]200 x -x^2= 40x + 3375[/tex]

Rearranging

[tex]x^2-160 x + 3375=0[/tex]

Solving for x

[tex]x=135,\ x=25[/tex]

Both values are valid, but only x=25 lies in the determined range for x, thus the only solution is

x=25