Question

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

R(x) = 5x - 0.0005x2. Find the marginal revenue at x = 1000.

17) The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal
average cost function.

Answer 1

Part 16) The marginal revenue is $4,000

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

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
`(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)