Question

The textbook solution for " Principle of Engineering Economic Analysis Edition 6th" by White, Case Pratt, seems to lack the step by step solution for problem chap 1- problem 30. Would you please provide it? Here is the problem

The process engineer at Strowbridge MetalWorks has the choice of machining a particular part on either of two machines. Orders for this part are received regularly, but the order size varies. When the order is processed on Manchine A, four sequential setup operations of 1 hour each are required. Once set up, the machining time is 0.50 hours per unit. When the order is processed on Machine B, eight sequential setup operations of 0.75 hours each are required. Once set up, the machining time per unit is 0.55 hours. The hourly wage rates for operators are $20 and $18 for Machine A and Machine B, respectively.
a. Which machine is preferred if the order size is 100 units?
b. Which machine is preferred id the order size is 500 units?
c. What is the breakeven order size?

Answer 1

a) Which machine is preferred if the order size is 100 units?

Machine A total cost for total unit is

Total hours required for setup of machine ( Four sequential steps) (1 hour * 4) = 4 hours.

Total Hours required for 100 units = (0.50 hours per unit * 100 units) = 50 hours.

Total hours for production of 100 units = ( 4 + 50) = 54 hours.

Total cost for 100 units = (54 hours * $20 per hour) = $1080

Machine B total cost for total units is

Total hours required for setup of machine ( Eight sequential steps) (0.75 hour * 8) = 6 hours.

Total Hours required for 100 units = (0.55 hours per unit * 100 units) = 55 hours.

Total hours for production of 100 units = ( 6 + 55) = 61 hours.

Total cost for 100 units = (61 hours * $18 per hour) = $1098

DECISION:

Machine A is better option for producing order size of 100 units since it has lower cost than machine B.

b) Which machine is preferred if the order size is 500 units?

Machine A

Total hours required for setup of machine ( Four sequential steps) (1 hour * 4) = 4 hours.

Total Hours required for 500 units = (0.50 hours per unit * 500 units) = 250 hours.

Total hours for production of 500 units = ( 4 + 250) = 254 hours.

Total cost for 500 units = (254 hours * $20 per hour) = $5080

Machine B

Total hours required for setup of machine ( Eight sequential steps) (0.75 hour * 8) = 6 hours.

Total Hours required for 500 units = (0.55 hours per unit * 500 units) = 275 hours.

Total hours for production of 500 units = ( 6 + 275) = 281 hours.

Total cost for 500 units = (281 hours * $18 per hour) = $5058

DECISION :

Machine B is the better option for the production of order size of 500 units. Since it has lower cost.

c) What is the break even order size?

Break even order size is the order size when there is no cost difference for the production of order size from either of the machine.

Break even order = Order cost cost in machine A = Order size cost in machine B

Let assume the order size is X

Order cost in machine A = (4 hours + X*0.50) * $20

Order cost in machine B = ( 6 hours + X * 0.55) * $18

Break even order size

= (4 hours + X*0.50) * $20 = ( 6 hours + X * 0.55) * $18......................... Solving the equation

= 80 + 10X = 108 + 9.9X

= X = 280 units .

Hence the break even order size is 280 units.