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C(x)=14x+1200
R(x)=23x
P(x)=23x-(14x+1200)

so P(X) isn't 9x-1200

The profit=revenue-cost. The cost has a variable part (14x) and a fixed part (1200).

In other words, P(x)=R(x)-C(x)

oh ok
so how would you find the average profit function AP(x)?

and smallest number of units needed to produce for a profit?

If I understand your question, then I get the following:
R(x)=px
R(x)=(-6x+100)x
R(x)=-6x^2+100x

R(x)=110x
Profit=Revenue-Cost
P(x)=110x-(60x+7500)
P(x)=110x-60x-7500
P(x)=50x-7500

yea. that's what I got, just wasn't sure about it
thanks

You're welcome