6. a companys revenue function is given by $r(x)=4x^{2}+12x$, and its expense function is $e(x)=2x^{2}+8x +…

6. a companys revenue function is given by $r(x)=4x^{2}+12x$, and its expense function is $e(x)=2x^{2}+8x + 10$. find the profit function $p(x)$. a $p(x)=2x^{2}+4x + 10$ b $p(x)=2x^{2}+4x - 10$ c $p(x)=4x^{2}-12x + 10$ d $p(x)=6x^{2}+20x - 10$

6. a companys revenue function is given by $r(x)=4x^{2}+12x$, and its expense function is $e(x)=2x^{2}+8x + 10$. find the profit function $p(x)$. a $p(x)=2x^{2}+4x + 10$ b $p(x)=2x^{2}+4x - 10$ c $p(x)=4x^{2}-12x + 10$ d $p(x)=6x^{2}+20x - 10$

Answer

  1. Recall the profit - function formula:
    • The profit function (P(x)) is given by (P(x)=R(x)-E(x)), where (R(x)) is the revenue function and (E(x)) is the expense function.
    • Given (R(x) = 4x^{2}+12x) and (E(x)=2x^{2}+8x + 10).
    • Then (P(x)=(4x^{2}+12x)-(2x^{2}+8x + 10)).
    • Expand the right - hand side: (P(x)=4x^{2}+12x - 2x^{2}-8x - 10).
    • Combine like terms: ((4x^{2}-2x^{2})+(12x - 8x)-10=2x^{2}+4x - 10).

Answer: b. (P(x)=2x^{2}+4x - 10)