Question

A production process consists of a three-step operation. The scrap rate is 20 percent for the first step and 10 percent for the other two steps.

a. If the desired daily output is 457 units, how many units must be started to allow for loss due to scrap? (Do not round intermediate calculations. Round up your final answer to the next whole number.)
Number of units
706
b. If the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? (Do not round intermediate calculations. Round up your final answer to the next whole number.)
Number of units
143
c. If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your final answer to the nearest whole number.)
Cost

Answer 1

a. The number of units that must be started to allow for loss due to scrap is approximately 635 units.

b. The reduced scrap rate would save approximately 535 units in terms of the scrap allowance.

c. The original scrap rate is costing the company approximately $1,777 per day.

How to calculate the number of units

a. To calculate the number of units that must be started to account for loss due to scrap, consider the scrap rates at each step.

The desired daily output is 457 units.

Step 1 scrap rate: 20%

Steps 2 and 3 scrap rate: 10%

First, calculate the number of units after the second and third steps by dividing the desired output by the proportion of units that survive these steps:

Units after second and third steps = Desired output / (1 - Second and third step scrap rate)

Units after second and third steps = 457 / (1 - 0.10)

Units after second and third steps = 457 / 0.90

Units after second and third steps ≈ 507.78

Next, calculate the number of units after the first step by dividing the units after the second and third steps by the proportion of units that survive the first step:

Units after first step = Units after second and third steps / (1 - First step scrap rate)

Units after first step = 507.78 / (1 - 0.20)

Units after first step = 507.78 / 0.80

Units after first step ≈ 634.72

Rounding up to the next whole number, the number of units that must be started to allow for loss due to scrap is approximately 635 units.

b. If the scrap rate for each step is cut in half at every operation, calculate the units saved in terms of the scrap allowance.

First step scrap rate: 20% (original)

Second and third step scrap rate: 10% (original)

Reduced scrap rate for each step:

First step scrap rate: 20% / 2 = 10%

Second and third step scrap rate: 10% / 2 = 5%

Using the same approach as in part a, calculate the new number of units that must be started:

Units after first step = 457 / (1 - 0.10) ≈ 507.78

Units after second and third steps = 507.78 / (1 - 0.05) ≈ 534.51

Rounding up to the next whole number, the reduced scrap rate would save approximately 535 units in terms of the scrap allowance.

c. If the scrap represents a cost of $10 per unit, calculate the cost to the company per day for the original scrap rate.

Number of units scrapped with the original scrap rate = Units after second and third steps - Desired output

Number of units scrapped = 634.72 - 457 ≈ 177.72

Cost per day = Number of units scrapped * Cost per unit

Cost per day = 177.72 * $10 ≈ $1,777

Therefore, the original scrap rate is costing the company approximately $1,777 per day.