Question #346413

The local convenience store makes personal pan pizzas. Currently, their process makes complete pizzas, fully cooked, for the customer. This process has a fixed cost of $20,000, and a variable cost of $1.75 per pizza. The owner is considering a different process that can make pizzas in two ways: completely cooked (as before), or partially cooked and then flash frozen, for the customer to finish at home. This alternate process has a fixed cost of $24,000, but a lower variable cost (because much less energy is used in baking) of $1.25 per pizza.

a. What is the crossover point between the existing process and the proposed process?

b. If the owner expects to sell 9,000 pizzas, should he get the new oven?

Expert's answer

Solution

a. The total cost equation for an existing process would be:

у = 20,000 + 1.75*х

where y is the total cost of pizza production for the existing process

x is the number of pizzas produced

$20,000 are fixed costs

$1.75 - variable costs

The equation of total costs for the proposed process will take the form:

у = 24,000 + 1.25*х

where y is the total cost of pizza production for the proposed process

x is the number of pizzas produced

$24,000 are fixed costs

$1.25 - variable costs

Where the total costs for both equations are equal is the point of their intersection. Therefore, we equate these equations to find the number of pizzas for which the total costs are equal.

20,000 + 1.75*х = 24,000 + 1.25*х

0.5*х = 4000

х = 4000/0.5 = 8000

Now, substituting the number of pizzas into one of the equations, we get the value of the total costs equal to both the existing process and the proposed process.

20,000 + 1.75 * 8000 = $34,000

b. Substitute 9,000 pizzas he wants to sell into the equation to get the total cost for the existing and proposed process.

20,000 + 1.75 * 9000 = $35750

24,000 + 1.25 * 9000 = $35250

The value of the total cost for the existing process when selling 9000 pizzas will be $35750, and for the proposed 35250.

It follows from this that the owner needs to purchase a new oven, since this will reduce the total cost by $500 when selling 9000 pizzas.

Answer

a. The intersection point between the existing process and the proposed process is 8000 pizzas and a total cost of $34000.

b. The owner should purchase a new oven when selling 9,000 pizzas, with a total cost of $500 less than the old oven.

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