Question

The price-demand and cost functions for the production of microwaves are given as p = 105 - q/90andC(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 profit function in terms of q.P(q) =(B) Evaluate the marginal profit function at q - 1000.P'(1000) =

Answer 1

Part A

`R=(105-(q)/(90))^q`
`R=105q-(q^2)/(90)`
`\begin{gathered} Profit=R-C=105q-(q^2)/(90)-(22000+90q) \\ \\ p(q)=-(q^2)/(90)+15q-22000 \end{gathered}`

Part B

`\begin{gathered} P^{^(\prime)}=-(q)/(45)+15 \\ \\ \\ p^{^(\prime)}(1000)=-(1000)/(45)+15^2 \\ P^{^(\prime)}(1000)=-22.22222+225 \\ P^{^(\prime)}(1000)=202.777777778 \end{gathered}`

The final answer

Part A

`P(q)=-(q^2)/(90)+15q-22000`

Part B

`P^{^(\prime)}(1000)=202.777778`