Question

16) The revenue (in thousands of dollars) from producing x units of an item is modeled by

Answer 1

Answer:

Part 16) The marginal revenue is $4,000

Part 17) The marginal average cost function is (70x+41)

Step-by-step explanation:

Part 16) we know that

The marginal revenue function is simply the derivative of the revenue function

we have

$R(x)=5x-0.0005x^{2}$

Find  $\frac{dR(x)}{dx}$

$R'(x)=5-0.001x$

For x=1,000 units

substitute

$R'(x)=5-0.001(1,000)$

$R'(x)=5-1=\ 4$

Remember that the units is in thousands of dollars

therefore

The marginal revenue is $4,000

Part 17) we know that

The marginal average cost function is simply the derivative of the average cost function

we have

$C(x)=(5x+3)(7x+4)$

Applying the distributive property

$C(x)=35x^2+20x+21x+12$

$C(x)=35x^2+41x+12$

Find the derivative

$C'(x)=70x+41$

therefore

The marginal average cost function is (70x+41)