To find the break-even quantity, we need to determine the value of $x$ at which the cost $C$ equals the revenue $R$.

The given equations are: $C = 73x + 660$ $R = 95x$

Step 1: Set $C$ equal to $R$

$73x + 660 = 95x$

Step 2: Solve for $x$

Rearrange the equation to isolate $x$: $660 = 95x - 73x$ $660 = 22x$

Divide both sides by 22: $x = \frac{660}{22}$ $x = 30$

Step 3: Verify the solution

Substitute $x = 30$ into the original equations for $C$ and $R$:

• $C = 73(30) + 660 = 2190 + 660 = 2850$
• $R = 95(30) = 2850$

Since $C = R$, the solution is correct.

Final Answer:

The break-even quantity is 30 units.

Would you like me to analyze further or help with part (b)? Here are some related questions:

1. What is the profit when selling 28 units?
2. How is the break-even point affected if the fixed cost changes?
3. What happens if the revenue per unit increases to 100?
4. Can the break-even quantity ever exceed the maximum units that can be sold?
5. How do you graphically represent the break-even analysis?

Tip: Break-even analysis is crucial for understanding how costs, revenue, and sales volume interact in business.