One afternoon a bakery finds that it has $300$ cups of  flour and $300$ cups of sugar on hand. Annie and Sam decide to use this to make and sell some batches of cookies and some cakes. Each batch of cookies will require $1$ cup of flour and $3$ cups of sugar. Each cake will require $2$ cups of flour and $1$ cup of sugar. Annie thinks that each batch of cookies should sell for $2$ dollars and each cake for $1$ dollar, but Sam thinks that each batch of cookies should sell for $1$ dollar and each cake should sell for $3$ dollars. Find the difference between the maximum dollars of income they can receive if they use Sam's selling plan and the maximum dollars of income they can receive if they use Annie's selling plan.

Let's think step by step and output the final answer within \boxed{}.
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