Please show all work, no coding.

Let S={a,b,c,d,e,f,g} be a collection of objects with benefit-weight values, a:(12,4),b:(10,6),c:(8,5),d:(11,7),e:(14,3),f:(7,1),g:(9,6). a) What is an optimal solution to the fractional knapsack problem for S assuming we have a sack that can hold objects with total weight 18 ? Show your work. Also, identify which objects are chosen and give the maximum profit. b) What is an optimal solution to the 0-1 knapsack problem for assuming we have a sack that can hold objects with total weight 18 ? Show your work. Also, identify which objects are chosen and give the maximum profit