Question

The price-demand and cost functions for the production of microwaves are given as p= 205 - q/70 and C(q) = 18000 + 20q,where q is the number of microwaves that can be sold at a price of p dollars per unit and C(q) is the total cost (in dollars) of producing q units.(A) Find the marginal cost as a function of q.C'(q)= (B) Find the revenue function in terms of q.R(q) =(C) Find the marginal revenue function in terms of q.R'(q)=

Answer 1

$\begin{gathered} p=205-\frac{q}{70} \\ C(q)=18000+20q \end{gathered}$

(A)

Find the derivative of C(q):

$\begin{gathered} C^{\prime}(q)=0+20(1) \\ C^{\prime}(q)=20 \end{gathered}$

(B)

The revenue function is:

$\begin{gathered} R(q)=q\cdot p \\ so: \\ R(q)=q(205-\frac{q}{70}) \\ R(q)=205q-\frac{q^2}{70} \end{gathered}$

(C)

The derivative of R(q) is:

$\begin{gathered} R^{\prime}(q)=205(1)-\frac{1}{70}(2q) \\ so: \\ R^{\prime}(q)=205+\frac{q}{35} \end{gathered}$