Hello, I have a question for the question 2 and question 3. I just dont know how to solve this budget problem. How does this form derive from?

Exercise 3 (A Boolean problem: of maximal margin) We have to decide which item tosell amongofacollection ofnitems, withgiven aellingprimss; >0, 1' = l,...,n. Selling implies a. transaction cost a; > 0 for each item 1'; the total transaction amt is the sum of these costs, plus a. xed muonnt d > 0 (any, d = I). We am interested in the following decision problem: which items need to be sold, in order to maximize the margin (revenutoto-ooet ratio). 1. Show that the problem canheformalimdma 8T1 is 4%. m), M} i 1m- 2- Show that the problem admits a. convex fmlmllntionlz p' 213131 t : t 3 1T(s tc)+. Hint: or given t 2 I], exprms the condition x) 5 t {or (may :1: E {0, 1}\" in simple terms. 3. How can we waiver an optimal solution :r', from an optimal value t\" for the alum: pmblem'