Removal of tax excise on producers, will increase supply? If the government removes an excise tax on producers, will their supply increase?

For example,


Price of gasoline is $2 a gallon 
Producers are taxed at 50 cents per gallon by the government
Weekly demand is 400 million gallons per week at 2 dollars a gallon
Weekly supply is 300 million gallons per week at 2 dollars a gallon


In essence if a excise is removed from the producers, to make gasoline more affordable. Would their supply increase as they are paying less to produce a gallon of gasonline?
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.