sir, my doubt is regarding q 3:
A firm is deciding whether to hire a worker for a day at a daily wage
of Rs. 20/-. If hired, the worker can work for a maximum of 10 hours
during the day. The worker can be used to produce two intermediate
inputs, 1 and 2, which can then be combined to produce a final good. If the worker produces only 1, then he can produce 10 units of input 1 in
an hour. However, if the worker produces only 2, then he can produce
20 units of input 2 in an hour. Denoting the levels of production of
the amount produced of the intermediate goods by k1 and k2 , the
production function of the final good is given by √k1k2. Let the final
product be sold at the end of the day at a per unit price of Rs. 1/-.
Solve for the firms optimal hiring, production and sale decision.

I tried solving it by assuming L1 labourers are used in pdtn of input 1 and L2 in input 2.
so, k1=10*10*L1
and k2+20*1o*L2
the cost of producing input 1= L1*20, the number of labourers multiplied by the dailly wage.
so, per unit cost of producing input 1=L1*20/(10*10*L1)=1/5
And sim for input 2, per unit cost= 1/10.

next, i found out the cost functioN:k2/k1=2, k2=2k1, putting it back ik the cobb douglas pdtn fun, k1=Q/sq root(2)
k2=Q*sq root(2)
and the cost fn= sq root(2)/ 5*Q

profit function= Q-sq root(2)/ 5*Q
however, this is an increasing function.. so how will we find the optimal values?
plz help.
thanks in advance.