Design an algorithm that calculates the sales tax and the price (amount due) of an item sold in a particular state. The sales tax is calculated as follows:

The state's portion of the sales tax is 4%

The city's portion of the sales tax is 1.5%

If the item is a luxury item, such as a car more than $50,000, then there is as 10% luxury tax.

Draw out a detailed problem analysis and the algorithm design.

Please show your steps neatly! I will rate thumbs up for the correct answer. Thank you in advance!