SOLUTION:
Step 1:
The price-demand and cost functions for the production of microwaves are given as:
[tex]\begin{gathered} \text{p = 105 -}\frac{q}{90} \\ and \\ C(q)\text{ = 22000 +90 q} \end{gathered}[/tex]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) =
[tex]\begin{gathered} Given\text{ p = 105 -}\frac{q^}{90} \\ Revenue,\text{ pq = 105 q -}\frac{q^2}{90}=\text{ R} \\ Then,\text{ R}^I=105\text{ -}\frac{q}{45} \\ R^I(\text{ 1000 \rparen =}105\text{ -}\frac{1000}{45} \\ R^I\text{ \lparen 1000 \rparen = }\frac{4725\text{ -1000}}{45}=\frac{3725}{45}=\text{ 82. 7778} \\ R^{I\text{ }}(1000\text{ \rparen = \$ 82.78} \end{gathered}[/tex]
