We will go step by step to answer each part of the question.

(a) Develop the revenue function and cost function

Let $x$ be the number of units produced and sold.

• Revenue function: Revenue is calculated as
  $TR = \text{Selling price per unit} \times x$ Given that the selling price per unit is $22, the revenue function is:

  $TR = 22x$

• Cost function: The total cost includes fixed costs and variable costs: $TC = \text{Fixed Cost} + (\text{Variable Cost per unit} \times x)$ Given that the fixed cost is $1190 and variable cost per unit is $5, the cost function is:

  $TC = 1190 + 5x$

(b) Determine the number of units required to break even

Break-even occurs when Total Revenue (TR) = Total Cost (TC).

$22x = 1190 + 5x$

Solving for $x$:

$22x - 5x = 1190$

$17x = 1190$

$x = \frac{1190}{17} = 70$

Thus, 70 units must be sold to break even.

(c) Compute the break-even point as a percent of capacity

The given capacity per period is 2500 units.

$\text{Break-even percentage} = \left( \frac{\text{Break-even quantity}}{\text{Capacity}} \right) \times 100$

$= \left( \frac{70}{2500} \right) \times 100$

$= 2.8\%$

Thus, the break-even point is 2.8% of capacity.

(d) Compute the break-even point in sales dollars

Break-even sales dollars are calculated as:

$\text{Break-even sales} = \text{Break-even quantity} \times \text{Selling price per unit}$

$= 70 \times 22$

$= 1540$

Thus, the break-even point in sales dollars is $1540.

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Would you like any step-by-step explanation or additional details?

Here are 5 related questions to explore:

1. How does an increase in fixed costs affect the break-even point?
2. What happens to the break-even point if the selling price increases?
3. How do we interpret a margin of safety in this context?
4. What is the contribution margin per unit, and how is it used in break-even analysis?
5. If the company wants to earn a profit of $2000, how many units should it sell?

Tip: The break-even analysis is crucial for understanding profitability and making business decisions about pricing and costs. 🚀