DSE 2011 Doubt

[SoniaKapoor]

A firm has an order to supply 20 units of output.It can divide its production across two different plants,1 and 2, with cost functions C1(q1)=q1^2 and C2(q2)=3q2^2.
The total order must be produced i.e. q1+q2=20.What should be the amount firm must produce in each plant to minimise cost?


Please help...M stuck here

[econ14]

is the answer 5 and 15..??

[econ14]

put mc1=mc2 .get q1 in terms of q2 .
put it in q1+q2=20

[The Villain]

Ans is q1=15 and q2=5

[Dreyfus]

This is an optimization problem with constraint ....all u hv to do is first write the total cost function i.e sum of c1 and c2 and den add contraint to it using lagrangian multiplier......so that tc func will b C=q1^2+3q2^2+μ(20-q1-q2).
As per first order conditions equate partial derivatives of C w.r.t q1, q2 & μ to 0.
And finally u will get the optimum values of q1 nd q2 i.e 15 nd 5 resp...

[don123]

CONTENTS DELETED

The author has deleted this message.