: Let's play a basic form of Scrabble! The rule, if you aren't aware already, are fairly simple. You are assigned an, ob ..., a, tiles from the English alphabet a, b,..., 2 respectively. Specifically, if ag = 5 then you can utilize the letter g at most 5 times to form your words. The only strict restriction being that these words must be in an English dictionary, say we use D to denote all the words in the Oxford English dictionary. Then, abacus E D, abode ED, zinc ED, basically D is the set of all English words. Suppose that for every word you construct, you obtain points equivalent to the length of that word. For example, if you are assigned ad = 1,ae = 2,an = 1, a = 2,a, = 1,2, = 4, y = 3,a, = 1,04 = 1, 2, = 2 i.e. (d, e, e, h,1,1,1,0,0,0,0,P.P.pr.t,y,y) and no other letter, you should construct words polyhedron and polytope scoring 18 points instead of den and pope scoring 7 points. For an assignment of letters (i.e., a, b,...., known), provide an linear (integer) program that will choose words so that your score is maximized. : Let's play a basic form of Scrabble! The rule, if you aren't aware already, are fairly simple. You are assigned an, ob ..., a, tiles from the English alphabet a, b,..., 2 respectively. Specifically, if ag = 5 then you can utilize the letter g at most 5 times to form your words. The only strict restriction being that these words must be in an English dictionary, say we use D to denote all the words in the Oxford English dictionary. Then, abacus E D, abode ED, zinc ED, basically D is the set of all English words. Suppose that for every word you construct, you obtain points equivalent to the length of that word. For example, if you are assigned ad = 1,ae = 2,an = 1, a = 2,a, = 1,2, = 4, y = 3,a, = 1,04 = 1, 2, = 2 i.e. (d, e, e, h,1,1,1,0,0,0,0,P.P.pr.t,y,y) and no other letter, you should construct words polyhedron and polytope scoring 18 points instead of den and pope scoring 7 points. For an assignment of letters (i.e., a, b,...., known), provide an linear (integer) program that will choose words so that your score is maximized