Question

The price-demand and cost functions for the production of microwaves are given as p= 105 - q/90and 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(g) is the total cost (in dollars) of producing q units. (A) Evaluate the marginal revenue function at q=1000.R'(1000) =(B) Find the profit function in terms of q.P(q) =(C) Evaluate the marginal profit function at q=1000.P'(1000) =

Answer 1

Step 1:

The price-demand and cost functions for the production of microwaves are given as:

`\begin{gathered} \text{p = 105 -}(q)/(90) \\ and \\ C(q)\text{ = 22000 +90 q} \end{gathered}`

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.

PART ONE:

a) Evaluate the marginal revenue function at q=1000.

R'(1000) =

`\begin{gathered} Given\text{ p = 105 -}(q^)/(90) \\ Revenue,\text{ pq = 105 q -}(q^2)/(90)=\text{ R} \\ Then,\text{ R}^I=105\text{ -}(q)/(45) \\ R^I(\text{ 1000 \rparen =}105\text{ -}(1000)/(45) \\ R^I\text{ \lparen 1000 \rparen = }\frac{4725\text{ -1000}}{45}=(3725)/(45)=\text{ 82. 7778} \\ R^{I\text{ }}(1000\text{ \rparen = \$ 82.78} \end{gathered}`