Question

ecoauto is a company that produces eco - friendly electric cars. the company has the following financial functions: - revenue function: $r(q)=300q - 3q^{2}$ where $q$ is the number of electric cars sold. - expense function: $e(q)=4,000 + 50q$ where $q$ is the number of electric cars produced. what is the profit equation $p(q)$ for ecoauto in terms of the quantity $q$ of cars produced and sold? $p(q)=-3q^{2}+300q - 4,000$ $p(q)=3q^{2}-250q + 4,000$ $p(q)=3q^{2}+250q - 4,000$ $p(q)=-3q^{2}+250q - 4,000$

Explanation:

Step1: Recall profit formula

Profit $P(q)=R(q)-E(q)$.

Step2: Substitute revenue and expense functions

$P(q)=(300q - 3q^{2})-(4000 + 50q)$.

Step3: Simplify the expression

$P(q)=300q-3q^{2}-4000 - 50q=-3q^{2}+(300q - 50q)-4000=-3q^{2}+250q - 4000$.

Answer:

$P(q)=-3q^{2}+250q - 4000$