A firm has $4$ plants that produce widgets. Plants A$,$ B$,$ and C can each produce $100$ widgets per day. Plant D can produce $50$ widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of $3$ customers. Customer $1$ requires $75$ units per day, customer $2$ requires $100$ units per day, and customer $3$ requires $175$ units per day.The shipping costs per widget for each possible route are shown in the table below: What is the minimum shipping cost?