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Two firms face a demand equation given by P=200,000 -6(Q1 + Q2) where Q1 and Q2 are the outputs of the two firms. The total cost equations for the...

Two firms face a demand equation given by P=200,000 -6(Q1 + Q2) where Q1 and Q2 are the outputs of the two firms.  The total cost equations for the two firms are given by: TC1 = 8000Q1 and TC2 = 8000Q2.  
If each firm sets its own output rate for profit maximization, and the other firm holds constant, what is the optimal output of each firm, as well as the optimal price for each firm.
Please show the work and/or formulas to derive the solution.

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P= 200,000 – 6(Q1+Q2)
TC1=8000Q1 ; TC2= 8000Q2
П1 = TR1 – TC1
= PQ1 – TC1
= 200,000Q1-6Q12-6Q2Q1-8000Q1
Partially differentiating w.r.t. Q1FOC: 200,000 -12Q1 – 6Q2 -8000 = 0
or, Q1* =...

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