Question

The price-demand and cost functions for the production of microwaves are given as p= 105 - q/90 and C(q) = 22000 + 90q,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(g) =(C) Find the marginal revenue function in terms of q.R'(q) =

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

• Marginal cost as a function of q.

,

• Revenue function in terms of q.

,

• Marginal revenue function in terms of q.

Given:

$\begin{gathered} p=105-\frac{q}{90} \\ \\ C\left(q\right)=22000+90q, \end{gathered}$

Part A

Marginal cost as a function of q:

$C^{\prime}(q)=\frac{d}{dq}(22000+90q)$$\begin{gathered} =0+90 \\ \\ =90 \end{gathered}$

Part B

Revenue function in terms of q.

Revenue = pq

$=(105-\frac{q}{90})q$$=105q-\frac{q^2}{90}$

Hence;

$R(q)=105q-\frac{q^2}{90}$

Part C

Marginal revenue function in terms of q.

$R^{\prime}(q)=\frac{d}{dq}(105q-\frac{q^2}{90})$$=105-\frac{2q}{90}$$=105-\frac{q}{45}$

Hence;

$R^{\prime}(q)=105-\frac{q}{45}$

ANSWER

A) C'(q) =90

B) R(q) = 105q - q^2/90

C) R'(q) = 105 - q/45