 Solution

Let $x_{ij}\ge 0$ be shipped amounts, with column sums equal to shop demand and row sums at most 15. Total demand is 42, so three units of warehouse stock need not be shipped. A feasible transportation problem allocation isIts row sums are $(15,15,12)$ and its column sums meet every demand. The cost is $18+18+12+3+4+10=65$.

For a transportation dual certificate with capacity inequalities, choose warehouse potentials $u=(0,-1,0)$ and shop potentials $v=(2,3,2,2,1)$. They have $u_i\le 0$ and $u_i+v_j\le c_{ij}$ for every cell. Any feasible allocation therefore hasThe second inequality has this direction because $u_i\le 0$ and warehouse use is at most 15. The exhibited allocation attains the lower bound, so the minimum cost is $\boxed{65}$.