DSE 2006 DOUBT

[SoniaKapoor]

DSE 2006 Q 29

A monopolist has 2 plants.
In plant 1 the total cost function is C1(q1)=2q1 and in plant 2 the total cost function is C2(q2)=q2^2/2 .
The dd curve faced by monopolist is p=10-q where q=q1+q2,
Find the values of q1 and q2.

Please help.

[SoniaKapoor]

pleaseeeeeeeeeeeeeee helpppppppp

[Dreyfus]

1388684507685.jpg1388684614360.jpg
This is also an optimization problem....as against to u previous question(cost minimization).....in this prob the objective of monopolist is to maximize profit.
Just formulate total revenue func, using demand fuction, and total cost func using individual cost funcs...see pic attached

[SoniaKapoor]

What will be the equation???

[Dreyfus]

Profit= Total Revenue- Total Cost
10q1+10q2-(q1+q2)^2-2q1-(q2^2)/2

[SoniaKapoor]

thank you....got it:-)))