Does the greedy algorithm always give an optimal solution in the system of denominations d(1) = 1, d(2) = 7, d(3) = 10? Justify your answer. (If you say yes, prove it; if you say no, give a counter example to show that the greedy algorithm does not give an optimal solution.)

If you say no, Please state what solution the system of denomination gives as the solution and then state and explain another counterexample