Programmers must be able to think logically and approach problem solving in logical steps or tasks. missing a step can have disastrous effects, so you should train yourself to think in a structured, logical way. this activity will encourage you to think in a logical step-by-step manner. you will list at least 10 steps for making a particular dish. when writing these steps, make sure you do not take anything for granted. assume that the person following your steps may have no knowledge of cooking. list your steps here

)a grad student comes up with the following algorithm to sort an array a[1..n] that works by first sorting the first 2/3rds of the array, then sorting the last 2/3rds of the (resulting) array, and finally sorting the first 2/3rds of the new array. 1: function g-sort(a, n) . takes as input an array of n numbers, a[1..n] 2: g-sort-recurse(a, 1, n) 3: end function 4: function g-sort-recurse(a, `, u) 5: if u ⒠` ≤ 0 then 6: return . 1 or fewer elements already sorted 7: else if u ⒠` = 1 then . 2 elements 8: if a[u] < a[`] then . swap values 9: temp ↠a[u] 10: a[u] ↠a[`] 11: a[`] ↠temp 12: end if 13: else . 3 or more elements 14: size ↠u ⒠` + 1 15: twothirds ↠d(2 ◠size)/3e 16: g-sort-recurse(a, `, ` + twothirds ⒠1) 17: g-sort-recurse(a, u ⒠twothirds + 1, u) 18: g-sort-recurse(a, `, ` + twothirds ⒠1) 19: end if 20: end function first (5 pts), prove that the algorithm correctly sorts the numbers in the array (in increasing order). after showing that it correctly sorts 1 and 2 element intervals, you may make the (incorrect) assumption that the number of elements being passed to g-sort-recurse is always a multiple of 3 to simplify the notation (and drop the floors/ceilings).

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The initial tableau of a linear programming problem is given. use the simplex method to solve it. x 1 x 2 x 3 s 1 s 2 z 1 2 4 1 0 0 8 3 4 1 0 1 0 10 minus3 minus12 1 0 0 1 0 the maximum is nothing when x 1equals nothing, x 2equals nothing, x 3equals nothing, s 1equals3, and s 2equals0. (be sure to simplify to lowest terms if necessary.)