You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
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A novice economist-cryptographer received a cryptogram from the ruler, which contained a new secret decree regarding the introduction of a per-unit tax on a certain market. The cryptogram indicated the total tax revenue that needed to be collected, also emphasizing that a greater sum of tax revenues could not be collected on this market. Unfortunately, the economist-cryptographer decoded the cryptogram incorrectly, misordering the digits in the total tax revenue. Based on the incorrect data, a decision was made to introduce a per-unit tax on the producer amounting to 90 monetary units per unit of goods. It is known that the market demand is given by \( Q_d = 688 - 4P \), and the market supply is linear. In a situation with no taxes, at the equilibrium point, the price elasticity of market supply is 1.5 times the modulus of the price elasticity of the market demand function. After the tax was introduced, the producer's price decreased to 64 monetary units.

1. Restore the market supply function.
2. Determine the total tax revenue that was collected with the chosen tax rate.
3. Determine the per-unit tax rate that would achieve the ruler's decree.
4. What is the amount of tax revenue that the ruler indicated to collect?
user
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A novice economist-cryptographer received a cryptogram from the ruler, which contained a new secret decree regarding the introduction of a per-unit tax on a certain market. The cryptogram indicated the total tax revenue that needed to be collected, also emphasizing that a greater sum of tax revenues could not be collected on this market. Unfortunately, the economist-cryptographer decoded the cryptogram incorrectly, misordering the digits in the total tax revenue. Based on the incorrect data, a decision was made to introduce a per-unit tax on the producer amounting to 90 monetary units per unit of goods. It is known that the market demand is given by \( Q_d = 688 - 4P \), and the market supply is linear. In a situation with no taxes, at the equilibrium point, the price elasticity of market supply is 1.5 times the modulus of the price elasticity of the market demand function. After the tax was introduced, the producer's price decreased to 64 monetary units.

1. Restore the market supply function.
2. Determine the total tax revenue that was collected with the chosen tax rate.
3. Determine the per-unit tax rate that would achieve the ruler's decree.
4. What is the amount of tax revenue that the ruler indicated to collect?
train