Let a monopolist has 8 stores in a city

 Let a monopolist has 8 stores in a city. Using Hotelling linear city model, calculate the Total Social Surplus (TSS) and profit of the monopolist. Can we say that TSS is at its maximum when the number of firms is four? Can we say that profit is maximised when the number of firms is seven? Justify your answers clearly. (Note: Use ALL of the assumptions from lecture note Chapter 10 and also following values for the parameters: R = $10; c = $2; N = 1000; t = $2; and F = $40 in your analysis).