The manager is tasked with developing a work schedule for both full-time and part-time staff to ensure there is adequate assistance on the day of promoting the new membership card. As a data analyst in the shopping mall, you have recommended the use of a mathematical model to determine the most efficient staff schedule. Important information related to this schedule is given below:

Event takes place from 11am to 9pm.

Each full-time staff starts on the hour and works a 3-hour shift, followed by 1 hour for lunch and then another 3-hour shift.

Minimum full-time staff required is 3.

There should always be at least one full-time staff on duty at all times.

$80 per hour for the full-time staff, and $50 per hour for part-time staff.

Part-time staff can work either 3-hour, 4-hour shift or a combination of both.

Formulate and determine an optimal schedule for the staff, taking into consideration the minimum number of staff required in each hour. Present your optimal schedule in a diagram.

Excel and Excel Solver need to be used for a solution.