Question

The function C(x)=600x-0.3x^2 represents the total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. what number of units would produce a maximum cost?

Answer 1

C(x)=- 0.3x^2+600x
y=ax^2+bx+c
it shows a upside down parabola equation.
to find maximum value we need to find its vertex(h,k)
as this is a standard quadratic equation we need to see parabolis equation too
y=a(x-h)^2+k
if u see this eq^n K would be the maximum value of Y if x=h.
where h,k are vertex of parabola.

h=-b/2a(derived standard formula)
C(x)=- 0.3x^2+600x
y=ax^2+bx+c
a= -0.3 b=600
h=-600/-0.3
h= 2000
put h in place of x to get K
K= -0.3(2000)^2+600(2000)
K= - 1200000+1200000
K=0

u gets k=0
means C(x)=0
600x= -0.3x^2
600= 0.3x
x=6000/3
x= 2000 units

Answer 2

What number of units would produce a maximum cost? 1,000

What is the maximum cost? 300,000$

Explanation:

I just did the assignment :)