Questions: Janelle Heinke, the owner of Ha'Peppas!, is considering a new oven in which to bake the firm's signature dish, vegetarian pizza. Oven type A can handle 22 pizzas an hour. The fixed costs associated with oven A are 22,500 and the variable costs are 2.50 per pizza. Oven B is larger and can handle 44 pizzas an hour. The fixed costs associated with oven B are 30,000 and the variable costs are 1.00 per pizza. The pizzas sell for 12.00 each. a) The break-even point in units for oven type A= units (round your response to the nearest whole number).

Janelle Heinke, the owner of Ha'Peppas!, is considering a new oven in which to bake the firm's signature dish, vegetarian pizza. Oven type A can handle 22 pizzas an hour. The fixed costs associated with oven A are 22,500 and the variable costs are 2.50 per pizza. Oven B is larger and can handle 44 pizzas an hour. The fixed costs associated with oven B are 30,000 and the variable costs are 1.00 per pizza. The pizzas sell for 12.00 each.
a) The break-even point in units for oven type A= units (round your response to the nearest whole number).

Transcript text: Janelle Heinke, the owner of Ha'Peppas!, is considering a new oven in which to bake the firm's signature dish, vegetarian pizza. Oven type A can handle 22 pizzas an hour. The fixed costs associated with oven $A$ are $\$ 22,500$ and the variable costs are $\$ 2.50$ per pizza. Oven $B$ is larger and can handle 44 pizzas an hour. The fixed costs associated with oven B are $\$ 30,000$ and the variable costs are $\$ 1.00$ per pizza. The pizzas sell for $\$ 12.00$ each. a) The break-even point in units for oven type $\mathrm{A}=$ $\qquad$ units (round your response to the nearest whole number).

Solution

Solution Steps

Step 1: Define the Variables

Let:

$ F_A = 22500 $ (fixed costs for oven type A)
$ V_A = 2.50 $ (variable cost per pizza for oven type A)
$ P = 12.00 $ (selling price per pizza)

Step 2: Set Up the Break-Even Equation

The break-even point occurs when total revenue equals total costs. The total cost $ C $ and total revenue $ R $ can be expressed as: \[ C = F_A + V_A \cdot x \] \[ R = P \cdot x \] where $ x $ is the number of pizzas.

Setting total costs equal to total revenue: \[ F_A + V_A \cdot x = P \cdot x \]

Step 3: Rearrange the Equation

Rearranging the equation to solve for $ x $: \[ F_A = P \cdot x - V_A \cdot x \] \[ F_A = (P - V_A) \cdot x \] \[ x = \frac{F_A}{P - V_A} \]

Step 4: Substitute the Values

Substituting the known values into the equation: \[ x = \frac{22500}{12.00 - 2.50} = \frac{22500}{9.50} \]

Step 5: Calculate the Break-Even Point

Calculating the value: \[ x \approx 2368.4211 \] Rounding to the nearest whole number gives: \[ x = 2368 \]