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Firm X is studying profitability of their new console. It costs this firm $5, 000, 000 + 100q^1.1 + 300q to produce q consoles per month.
Firm X has decided to price its console so that it takes a 5% loss on the variable costs of each console (and does not factor fixed costs into its pricing scheme at all, choosing to recoup that in other ways). They do so with the understanding that they can make up for that loss through licensing and game sales.
After conducting market research, they estimate that the monthly demand for the console is given by q = 400, 000 - 450p.
Find the equilibrium price and quantity for monthly sales of the console.
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