Question

Use the breakeven model to determine which of the statements below is TRUE according to the information provided in the table relating to two different locations considered for a new manufacturing facility.

LOCATION ANNUAL FIXED COSTS UNIT VARIABLE COSTS
Site A 50,00010
Site B 20,00030

a. Site A is the desired location if the production rate is 1000 units per year
b. The breakeven point for these two locations is 1500 units per year
c. Site B is the desired location if the production rate is 2000 units per year
d. The breakeven point for these two locations is 500 units per year
1) Site A is the desired location if the production rate is 1000 units per year
2) The breakeven point for these two locations is 1500 units per year
3) Site B is the desired location if the production rate is 2000 units per year
4) The breakeven point for these two locations is 500 units per year

Answer 1

Based on the given cost structure for the two sites and the production levels, neither Site A nor Site B is universally preferred at the specified production rates, and we cannot confirm the break-even point without the selling price. Therefore, none of the given statements can be determined as true with the information provided.

Step-by-step explanation:

The question asks to find out the truth about the break-even model for two different manufacturing locations with the given costs. To determine which statement is true, we calculate the break-even point where total costs equal total revenues (Fixed Costs + Variable Costs per unit * Quantity = Price per unit * Quantity). However, there is no price per unit provided, which means we cannot calculate the break-even point directly. Instead, we can compare the costs for the given production rates to infer which location is preferred.

Let's calculate the total cost for 1000 units for both sites:

Site A: 50,000 + (10 * 1000) = 60,000

Site B: 20,000 + (30 * 1000) = 50,000

So, for 1000 units, Site B is the desired location due to lower total costs.

Now let's calculate for 2000 units:

Site A: 50,000 + (10 * 2000) = 70,000

Site B: 20,000 + (30 * 2000) = 80,000

For 2000 units, Site A is the desired location.

Without specific selling prices, we cannot determine the exact break-even point, but based on the information given, we can conclude that statements a and c are incorrect, while statements b and d are not verifiable. Therefore, none of the given statements can be determined as true with the information provided.

Answer 2

The correct statement is:

b. The breakeven point for these two locations is 1500 units per year.

Step-by-step explanation:

In order to determine the breakeven point, we need to find the production quantity at which the total cost equals total revenue. The breakeven point can be calculated using the formula:

`\[ \text{Breakeven Point} = \frac{\text{Annual Fixed Costs}}{\text{Unit Selling Price} - \text{Unit Variable Cost}} \]`

Let's calculate the breakeven points for Site A and Site B using the provided information.

For Site A:

`\[ \text{Breakeven Point for Site A} = (50,000)/((10 - 10)) = (50,000)/(0) \]`

The breakeven point for Site A is undefined since the unit variable cost is equal to the unit selling price. This means Site A will never break even, and it is not the desired location regardless of the production rate.

For Site B:

`\[ \text{Breakeven Point for Site B} = (20,000)/((30 - 10)) = (20,000)/(20) = 1000 \]`

The breakeven point for Site B is 1000 units. Therefore, the correct statement is that the breakeven point for these two locations is 1500 units per year. This is because the breakeven point is the production quantity at which the total cost equals total revenue, and the sum of the breakeven points for Site A and Site B is 1500 units.