Indoor Life,a TV Periodical Sells Subscriptions (Q)and Advertising Spaces (N)

Indoor Life,a TV periodical sells subscriptions (Q)and advertising spaces (N).The demand curve for subscriptions is
p = 50 - 0.002Q - 0.001N²
The magazine has negligible costs of printing and writing (the editor basically sits at home and watches TV),so the production costs are said to be zero.
The advertising is sold in a competitive market.The price advertisers pay (per unit of N)is based on the number of subscriptions the magazine sells times 0.001.Thus the market price for advertising spots can be represented with the equation:
pN = 0.01Q
Compute the optimal number of subscriptions and advertisements for the magazine.

Correct Answer:

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Let's write out the monopolist's profit ...

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