Minimum wage has zero impact on the cost of goods. Price gauging to maintain a profit margin is what impacts the cost of goods.

All costs affect the prices of goods and services. Wages. Fuel cost. Insurance. Taxes. All of the costs impact the prices. The producer has to recoup all of the costs of production in order to make a profit.

And lets be honest, minimum wage jobs are for school kids making pocket money not for somebody trying to make a living. If you are trying to support yourself with a minimum wage job you need to be out job hunting.