A manufacturer of chemical glassware needs to purchase a certain amount of raw material. The profit, $p$, in dollars expected from purchasing $t$ tons of raw material, where $t$ is positive, is: \[ p=50,000(2 t-1)(t-5) \] What is the smallest amount of raw material in tons that the manufacturer can purchase to break even with a profit of 0 dollars?

Step 1 ：The manufacturer of chemical glassware needs to purchase a certain amount of raw material. The profit, $p$, in dollars expected from purchasing $t$ tons of raw material, where $t$ is positive, is given by the equation \(p=50,000(2 t-1)(t-5)\).

Step 2 ：The manufacturer breaks even when the profit is zero. So, we need to solve the equation \(p=50,000(2 t-1)(t-5) = 0\) for $t$. This equation will have two solutions, as it is a quadratic equation in $t$.

Step 3 ：We are interested in the smallest positive solution, as $t$ represents the amount of raw material in tons, which cannot be negative.

Step 4 ：Solving the equation gives us two solutions: \(t = 1/2\) and \(t = 5\).

Step 5 ：The smallest positive solution is \(t = 1/2\).

Step 6 ：Final Answer: The smallest amount of raw material in tons that the manufacturer can purchase to break even with a profit of 0 dollars is \(\boxed{0.5}\).