Question 1136532
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<pre>
The cost function to make n hats is


    C(n) = 42*n + 243   dollars.


The revenue function is


    R(n) = 69*n  dollars.


The break event equation/inequality is


    R(n) >= C(n),   or

    69*n >= 243 + 42*n.


Simplify and solve for n:


    (69-42)*n >= 243

    27n >= 243  ===============>  n >= 243/27 = 9.


<U>ANSWER</U>. 9 hats.
</pre>

Solved.