Question

An artist makes a profit of $(500p-p^2)$ dollars from selling $p$ paintings. What is the fewest number of paintings the artist can sell to make a profit of at least $\$60,000$?

• A. $100$
• B. $150$
• C. $200$
• D. $300$
• E. $600$

Answer 1

Answer: (C)

$200$

To find the fewest number of paintings,

consider, $60000=500p-p^2$

$\Rightarrow p^2-500p+60000=0$

$\Rightarrow p^2-200p-300p+60000=0$

$\Rightarrow p(p-200)-300(p-200)=0$

Either $p-300=0$ or $p-200=0$

Either $p=300$ or $p=200$

Since it is asked for the fewest number of paintings the artist can sell to make a profit of atleast $\$60000$, therefore the answer is $200$.

Hence, option $C$ is correct.