Question

The price-demand and cost functions for the production of microwaves are given as p = 250 - q/40and C(q) = 90000 + 80q,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 cont (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

Question A: Find the marginal cost as a function of q.

Given the following equation : C(q) = 90,000 + 80q

The marginal cost, C'(q0), will be:

C(q) = 90,000 + 80q

C'(q) = 0 + 80(1)

C'(q) = 80

Therefore, C'(q) = 80

Question B: Find the revenue function in terms of q.

The revenue function should be: (No. of microwaves sold) x (Price of microwave)

Where the equation for the price of the microwave is given at p = 250 - q/40.

Thus, the formula will be:

$\text{ R\lparen q\rparen = q x p = \lparen q\rparen\lparen250 - }\frac{\text{ q}}{40})\text{ = 250q - }\frac{\text{ q}^2}{40}$

Therefore,

$\text{ R\lparen q\rparen = 250q - }\frac{\text{ q}^2}{40}$

Question C: Find the marginal revenue function in terms of q.

$\text{R\operatorname{\lparen}q\operatorname{\rparen}=250q}\frac{(\text{q})^{2}}{40}$$\text{R'}\operatorname{\lparen}\text{q}\operatorname{\rparen}\text{=\lparen250\rparen\lparen1\rparen- }\frac{\text{q}^(2)}{40}\text{ = 250 - }\frac{\text{ q }}{20}$

Therefore,

$\text{ R'\lparen q\rparen= 250 - }\frac{\text{ q }}{20}$