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-(q)/(90) \\ \\ C\left(q\right)=22000+90q, \end{gathered}`

Part A

Marginal cost as a function of q:

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

Part B

Revenue function in terms of q.

Revenue = pq

`=(105-(q)/(90))q`
`=105q-(q^2)/(90)`

Hence;

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

Part C

Marginal revenue function in terms of q.

`R^(\prime)(q)=(d)/(dq)(105q-(q^2)/(90))`
`=105-(2q)/(90)`
`=105-(q)/(45)`

Hence;

`R^(\prime)(q)=105-(q)/(45)`

ANSWER

A) C'(q) =90

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

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