Anovatech provides cloud computing services to other businesses. It uses programmers (labor) and servers (capital) to produce its services. It costs Anovatech $6,000 a month to hire a programmer, and $200 a month to rent a server. (For simplicity, assume all inputs are continuously divisible.) Today, Anovatech has 64 servers in their datacenters.

Anovatech can use servers to provide more service, or they can hire programmers to think of ways to run those servers more efficiently. Anovatech's production function is proportional to the sum of the square roots of the number of programmers they employ and the number of servers they rent, so assume thatQ=K+ L for some unit of output service.

In the short run, if Anovatech has a monthly budget of $200,000, what is the highest production they can achieve?

Anovatech management thinks that cost is a bit steep in the short run, but maybe in the long run they can bring the cost down.

In the long run, what is the lowest cost at which Anovatech would be able to produce 30 units a month of service?

How many programmers and servers would they employ?

L=

K=

What percent cost savings does this represent, relative to the short term?