I need help solving this problem:

Consider a closed economy with a large number of consumers. Each consumer has an initial endowment of 24 hours of time which can be consumed as leisure or sold in the labor market. Besides leisure (commodity 1), the consumer also needs food (commodity 2). All consumers have identical preferences, each having the utility function u(x₁,x₂) = Min{x₁,x₂}

a) Assume that the hourly wage is 100, while the price of one unit of food is also 100; which consumption plan is optimal for a (representative) consumer agent, and how many hours does she work?

The Minister of Finance, Don Cory, introduces a tax on wage earnings, demanding that each employee pays 50 % in taxes, lowering the after-tax wage rate to 50. Commenting on this new taxhe says: "The economic models used by the economists of my ministry suggest that this tax will not hurt employment, which, I am confident, will remain strong".

b) Identify the labor supply curve for a representative consumer to consider ifthe minister'sclaim correct.

I am unsure how to solve the utility function, since it is not differentiable..