Based on the information that can be gotten from the question, the price that should be charged by the theater for the matinee ticket will be $7.
From the complete information, when the price is $4 and the 3 customers enjoy the movie, the profit will be:
= ($4 - $1.5) × 3
= $2.5 × 3
= $7.5
Now, let's assume that the price charged is $7 and 2 customers enjoy the movie, the profit will be:
= ($7 - $1.5) × 2
= $5.5 × 2
= $12
Now, when the price is $12 and only 1 customer enjoyed the movie, the profit will be:
= ($12 - $1.5) × 1
= $10.5
It can be depicted that the profit of the theater will be at maximum when the price that is charged is $7.
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