The Law of Supply states that as prices increase the quantity supplied by producers will?

You have to remember that there are two religions called "ECONOMICS". One is based on reality and human nature, the other uses the same charts turned sideways because that leads to apparent justification of tax-and-spend policies. Therefore the government always uses the second religion and anybody who has to make a profit uses the first. Answers depend on which system you use.

Using traditional, or "Austrian", theories, if the retail price rises, producers would like to sell more. Increased inventory in stores tends to make buyers think they should pay less. So the system is self balancing.

The other set of theories, called "Keynesian", is not that sensible and was thoroughly discredited even while Nixon was still in office. If you are taking a course in Keynesian Economics, you should augment your studies at mises.org -- There is a flood of free material at that site and they also offer formal classes at a bargain rate: academy.mises.org/courses/curriculum/