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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) =

Respuesta :

Part A

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

Part B

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

The final answer

Part A

[tex]P(q)=-\frac{q^2}{90}+15q-22000[/tex]

Part B

[tex]P^{^{\prime}}(1000)=202.777778[/tex]

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