Question

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 20 pizzas an hour. The fixed costs associated with oven A are $20,000 and the variable costs are $2.00 per pizza. Oven B is larger and can handle 40 pizzas an hour. The fixed costs associated with oven B are $30,000 and the variable costs are $1.25 per pizza. The pizzas sell for $14 each.

a) What is the break-even point for each oven?

b) If the owner expects to sell 9,000 pizzas, which oven should she purchase?

c) If the owner expects to sell 12,000 pizzas, which oven should she purchase?

d) At what volume should Janelle switch ovens?

Answer 1

Answer:

a) Oven A  = 1,667; Oven B = 2,353 pizzas.

b) Oven A

c) Oven A

d) 13,334 pizzas

Explanation:

Since nothing was mentioned regarding her time availability, the capacity of each oven will not be taken into account.

The income equation for ovens A and B, respectively, are:

$A=(14-2)x-20,000\\B=(14-1.25)x-30,000$

Where 'x' is the number of pizzas sold.

a) The break-even occurs when income is zero:

$A=0=(14-2)x-20,000\\x_A=1,666.66\\B=(14-1.25)x-30,000\\x_B=2,352.94$

Rounding up to the next whole pizza, the break-even for oven A is 1,667 pizzas and for oven B it is 2,353 pizzas.

b) For x = 9,000:

$A=(14-2)*9,000-20,000\\A=\ 88,000\\B=(14-1.25)*9,000-30,000\\B=\ 84,750$

Income is greater with oven A, so Janelle should use oven A.

c) For x = 12,000

$A=(14-2)*12,000-20,000\\A=\ 124,000\\B=(14-1.25)*12,000-30,000\\B=\ 123,000$

Income is greater with oven A, so Janelle should use oven A.

d) She should switch ovens at the value for 'x' that causes B to be greater than A:

$A<B\\(14-2)*x-20,000<(14-1.25)*x-30,000\\10,000<0.75x\\x>13,333.33$

Rounding up to the next whole pizza, she should switch ovens at a volume of 13,334 pizzas.