Need help with this problem. thank you

Consider two goods: blue pens (good 1) and black pens (good 2). The principals of three different schools are trying to figure out how many pens to order, each for their own school.

Last year, the unit price of blue pens was $1 and the unit price of black pens was $2. The income that each school is approved to spend on these two goods is $2,000. In principle, it is expected that this allowance will remain unchanged this year. However, the price of blue pens has quadrupled, reaching a level of $4 (the price of black pens remains $2). You are asked to calculate for each of the three principals:

(i) last year's choice;

(ii) this year's choice;

(iii) a breakdown of the change in demanded amounts into substitution and income effects using the Hicks method; and

(iv) the money transfer requested by each school so as to remain indifferent, at the new prices, to last year's situation.

The preferences of the three principals are represented by the following utility functions:

(a) Principal David:u(x₁, x₂) =x₁x₂.

(b) Principal Lucy:u(x₁, x₂) = min{x₁,2x₂}.

(c) Principal Sam:u(x₁, x₂) =x₁+x₂.