MATH SOLVE

3 months ago

Q:
# 16) The revenue (in thousands of dollars) from producing x units of an item is modeled byR(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 marginalaverage cost function.

Accepted Solution

A:

Answer:Part 16) The marginal revenue is $4,000Part 17) The marginal average cost function is (70x+41)Step-by-step explanation:Part 16) we know thatThe marginal revenue function is simply the derivative of the revenue functionwe have[tex]R(x)=5x-0.0005x^{2}[/tex]Find Β [tex]\frac{dR(x)}{dx}[/tex][tex]R'(x)=5-0.001x[/tex]For x=1,000 unitssubstitute[tex]R'(x)=5-0.001(1,000)[/tex][tex]R'(x)=5-1=\$4[/tex]Remember that the units is in thousands of dollarsthereforeThe marginal revenue is $4,000Part 17) we know thatThe marginal average cost function is simply the derivative of the average cost functionwe have[tex]C(x)=(5x+3)(7x+4)[/tex]Applying the distributive property[tex]C(x)=35x^2+20x+21x+12[/tex][tex]C(x)=35x^2+41x+12[/tex]Find the derivative[tex]C'(x)=70x+41[/tex]thereforeThe marginal average cost function is (70x+41)