Option 2) The amount of product needed to generate the same profit is four thousand.
What is profit?
The money that remains after paying your company expenditures is your profit. Gross profit, operational profit, and net profit are the three primary forms of profit. The largest profit is gross. The amount left over after paying for the sold products and services is displayed.
Given the polynomial function as;
[tex]P(t)=-3t^{3}+12t^{2} +3t[/tex]
P(t) is the company's profit = $12 million
therefore,
[tex]P(t)=-3t^{3}+12t^{2} +3t=12\\-3t^{3}+12t^{2} +3t-12=0[/tex]
factorizing:
[tex](-3t+12)(t^{2}+ t^{2}) -(-3t+12)=0\\(-3t+12)(2t^{2}+1)=0\\[/tex]
[tex]t=4[/tex]
the company produces 1 thousand products
[tex]=4/1[/tex]
[tex]=4 thousand[/tex]
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