Question

The function C(x) = 600x – 0.3x2 represents 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?  What is the maximum cost?

Answer 1

max cost is the vertex
in the form
y=ax^2+bx+c
the xvalue of the vertex would be -b/2a

we have
C(x)=-0.3x2+600x
a=-0.3
b=600
xvalue of vertex=-600/(2 times -0.3)=1000
that is the numbe rof units

to get the cost, plug it for x
C(1000)=600(1000)-0.3(1000)^2
C(1000)=300,000



the number of units is 1000
the max cost is $300,000

Answer 2

1000 number of units would produce maximum cost.

Maximum cost = 300000

Explanation:

Given that total costs for a company to produce a product x as C(x) = 600x – 0.3x²

At maximum cost derivative of C(x) is zero.

C'(x) = 600 – 0.6x = 0

0.6x = 600

x = 1000

1000 number of units would produce maximum cost.

Maximum cost = C(1000) = 600 x 1000 – 0.3 x 1000² = 300000