I need help with his question below:

Question

The cost of running an assembly line can be modelled by the function C9x)=0.3x^2 - 0.9x + 1.675. where C(x) is the cost per hour in thousands of dollars and x is the number of items produced per hour in thousands. the most economical production level occurs when 1500 items are produced. Verify this using the appropriate calculations for rate of change in cost.

Answer 1

 

0 =  dC/dx = 0.6*X - 0.9 = 0

 

So

X=9/6 = 3/2 =1.5

 

So yes, the optimal production is 1.5k = 1500 units

 

 C(1.5) = 1

So the optimal production of 1500 units shall cost $1000 per hour