You are an executive for Super Computer, Inc. $($SC$),$ which rents out super computers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of $P$ cents per second. SC has two types of potential customers of equal number$-10$ businesses and $10$ academic institutions.

Each business customer has the demand function:

$Q=10-P$

where $Q$ is in millions of seconds per month; each academic institution has the demand:

$Q=8-P.$

The marginal cost to $SC$ of additional computing is $2$ cents per second, regardless of volume.

a$.$ Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What would be your profits? $($Round all answers to the nearest integer$)$

For business users, the rental fee would be $ per month and the usage fee is cents per second.

For academic institutions, the rental fee would be $ per month and the usage fee is cents per second. SC$\text{'}$s total profits are $ per month.