Your company, "TechSpark Solutions," specializes in providing software subscription packages for small businesses. Currently, you offer two subscription tiers: Professional and Enterprise.

The Professional Tier costs $$30$ per account per month to provide.

The Enterprise Tier costs $$50$ per account per month to provide.

You have two types of customers: Startups and Established Businesses.

Startups:

Willing to pay $$75$ per account per month for the Professional Tier and $$90$ per account per month for the Enterprise Tier.There are $200$ Startups in your market.

Established Businesses:

Willing to pay $$100$ per account per month for the Professional Tier and $$150$ per account per month for the Enterprise Tier.There are $150$ Established Businesses in your market.

Questions:

$($a$)$ What price will you charge for each subscription tier to maximize your profits?

Hint: Consider the willingness to pay of each customer type and how to segment the market for maximum profitability.