Question

The revenue function of a firm is given as \[ R=300000+2250x-75x^{2} \] Where $R$ is the revenue and $x$ is the quantity sold. The revenue maximizing level of quantity sold is:

• A. 5.47 units
• B. 15 units
• C. 30 units
• D. 45 units

Hint:

Logic Tip: For quadratic functions of the form $ax^2+bx+c$, maximum occurs at $x=-\frac{b}{2a}$ when $a<0$.

Answer 1

The Correct Option is B

Step 1:
Given: \[ R=300000+2250x-75x^{2} \] This is a quadratic function.

Step 2:
Revenue is maximum when: \[ \frac{dR}{dx}=0 \] Differentiate revenue function: \[ \frac{dR}{dx}=2250-150x \]

Step 3: x
Set derivative equal to zero: \[ 2250-150x=0 \] \[ 150x=2250 \] \[ x=15 \]

Step 4:
Therefore, revenue is maximum at: \[ \boxed{15 \text{ units}} \] Hence, the correct answer is: \[ \boxed{\text{(2) 15 units}} \]