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Nagle​ Electric, Inc., of​ Lincoln, Nebraska, must replace a robotic Mig welder and is evaluating two alternatives. Machine A has a fixed cost for the first year of

​$78,000 and a variable cost of ​$1414​, with a capacity of 16,000 units per year. Machine B is​slower, with a speed of​one-half of​ A's, but the fixed cost is only $57,000. The variable cost will be​ higher, at ​$1818 per unit. Each unit is expected to sell for ​$2525.

​a) What is the crossover point​ (point of​ indifference) for the two​ machines? _________

The crossover point for the two machines is _____ and _______ units. ​(Round your response to the nearest whole​number.)

​b) What is the range of units for which machine A is​preferable?

Machine A is preferable at a level of production

_____and ______ units.

units. ​(Enter your response as a whole​ number.)

​c) What is the range of units for which machine B is​preferable?

Machine B is preferable at a level of production ____ and ______ units

​(Enter your response as a whole​ number.)

Respuesta :

Answer:

(i) 5,250 units

(ii) above 5,250 units

(iii) below 5250 units ; 0 and 5249 units

Explanation:

Given ,

Machine A

Fixed cost = $78,000

Variable cost = $14

Capacity = 16,000 units

Total cost = Fixed cost + Variable cost × no. of units

Total cost = $78,000 + 14Q

Machine B

Fixed cost = $57,000

Variable cost = $18

Total cost = Fixed cost + Variable cost × no of units

Total cost = $57,000 + 18 Q

a) Cross over point is the point where total cost is equal

Cross over point = Q

$78,000 + 14 Q = $57,000 + 18 Q                    

78,000 – 57,000 = 4Q

21000 = 4Q

Q = 5250 units

Crossover point for the two machines is 5,250 units

b) Machine A is preferable above 5,250 units

Machine A is preferable at a level of production above 5,251 units

c) Machine B is preferable below 5250 units

Machine B is preferable at a level of production 0 and 5249 units

(i) 5,250 units

(ii) above 5,250 units

(iii) below 5250 units ; 0 and 5249 units

Calculation of the cross over point, range:

Since

For Machine A

Fixed cost = $78,000

Variable cost = $14

Capacity = 16,000 units

We know that

Total cost = Fixed cost + Variable cost × no. of units

Total cost = $78,000 + 14Q

For Machine B

Fixed cost = $57,000

Variable cost = $18

So,

Total cost = Fixed cost + Variable cost × no of units

Total cost = $57,000 + 18 Q

a) Cross over point refers to the point where the total cost should be equal

Here we assume Cross over point = Q

So,

$78,000 + 14 Q = $57,000 + 18 Q                    

78,000 – 57,000 = 4Q

21000 = 4Q

Q = 5250 units

b) Machine A should be preferable at a level of production above 5,251 units

c) Machine B should be preferable at a level of production 0 and 5249 units

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