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A how much output does each firm choose in the nash

Suppose there are two firms in a market who each choose a quantity of output to produce. Firm 1's quantity is q₁, and firm 2's quantity is q₂. Firm 1 chooses their quantity, q₁, first. Firm 2 observes q1, and then chooses their quantity, q₂. The market quantity is Q = q₁ + q₂. The market demand curve is given by P = 1000 - 5Q. Also, each firm has constant marginal cost equal to 100. There are no fixed costs.

The marginal revenue of the two firms are given by:

MR₁ = 1000 - 10q₁ - 5 q₂

MR₂ = 1000 - 5q₁ - 10q₂.

a) How much output does each firm choose in the Nash equilibrium?

b) What is the market price?

c) How much profit does each firm make?

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