Removal of tax excise on producers, will increase supply?
A producer will always maximize profit by setting marginal cost equal to marginal benefit. Removing an excise tax will reduce the cost of every gallon of gas, so it would indeed effectively lower the marginal cost of production. Assuming the production function isn't falling into a diseconomy of scale (where the more effort/resources you put it, the less efficiently you produce), then yes, production of gasoline should increase as a result.

Hope this helped.