Why does the price increase when the supply is perfectly inelastic and there is a subsidy to the producer?

A perfectly inelastic supply curve is a vertical upward sloping line. The perfectly inelastic curve represents that even infinite change in the price for the commodity does not cause any impact on the quantity distributed for the commodity. In case the product is perfectly inelastic in supply and subsidy is provided on it, there will be a rise in the price of the commodity. The reason being that with the subsidy the supply in the market cannot be increased. There is no change in the quantity supplied hence the prices tend to rise instead of falling because the higher prices generate more producer surplus.