Please explain each step with full explanation

There are two types of workers in a labor market, strong types (S) and weak types (W). Workers have hidden information about their type, meaning they know whether they are strong or weak, but the monopoly that is hiring workers in this industry does not observe this information. Nature makes a worker strong with probability 0.4 and weak with a probability 0.6. Strong types and weak types have the following respective total cost functions:

cs(x) = 20 + x2

cw(x) = 20 + 3x2

Each unit is worth $50 to the firm. Workers have an outside option equal to $10.

1- Write down the monopolist's problem and solve for the monopolist's optimal menu of output-payment combinations, where both strong and weak types participate.

2- What is the monopolist's expected profit when it offers this menu?

3- How much higher would the monopolist's expected profit be if there was no hidden information and the monopolist could offer a contract to a worker with full knowledge of the worker's type