A certain skincare company's profit in millions of dollars, P(t) is modelled by;
[tex]P(t)=-2t^3+8t^2+2t[/tex]
where t represents the number of quantity of skincare items produced, in thousands.
Today, the company produces 4 thousand products for a profit of $8 million.
Mathematically,
[tex]t=4,P(t)=8[/tex]
Thus, we would find the other quantity that gives same profit with the equation;
[tex]8=-2t^3+8t^2+2t[/tex]
Simplifying further, we have;
[tex]-2t^3+8t^2+2t-8=0[/tex]
From the previous statement,
[tex](t-4)[/tex]
is a factor. Thus, we have;
[tex]\begin{gathered} -2t^3+8t^2+2t-8=0 \\ -2(t-4)(t^2-1)=0 \end{gathered}[/tex]
Hence, the other quantity of product would be;
[tex]\begin{gathered} t^2-1=0 \\ t^2=1 \\ t=\pm1 \\ \text{Discard the negative value;} \\ t=1 \end{gathered}[/tex]
CORRECT OPTION: 1 thousand
