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A production process consists of a three-step operation. The scrap rate is 11 percent for the first step and 9 percent for the other two steps.

a.If the desired daily output is 452 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:

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:

c.If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your final answer to the nearest whole number. Omit the "$" sign in your response.)

Cost: $

Explanation / Answer

In a production process scrap is referred as the discarded or rejected material involved in an operation which in fact is appropriate for reprocessing. Scraps are expensive as it entails the left over materials engaged in a production process which would require further rework. In the given case the production process consists of a three-step operation:

Input – Scrap = Output

Desired daily output = 452 units

a.

Step 1 = Scrap rate 11%

Input units = 100 – 11 = 89

Thus Input units = 507.87 units

(452 units / 89 x 100)

Step 2 = Scrap rate 9%

Input units = 100 – 9 = 91

Thus Input units = 558.10 units

(507.87 units / 91 x 100)

Step 3 = Scrap rate 9%

Input units = 100 – 9 = 91

Thus Input units = 613.30 units or rounded off = 613 units

(558.10 units / 91 x 100)

b.

Step 1 = Scrap rate 5.5%

Input units = 100 – 5.5 = 94.5

Thus Input units = 478.31 units

(452 units / 94.5 x 100)

Step 2 = Scrap rate 4.5%

Input units = 100 – 4.5 = 95.5

Thus Input units = 500.85 units

(478.31 units / 95.5 x 100)

Step 3 = Scrap rate 4.5%

Input units = 100 – 4.5 = 95.5

Thus Input units = 524.45 units or rounded off = 524 units

(500.85 units / 95.5 x 100)

Thus savings would be: 613 units – 524 units = 89 units

c.

Step 1

Scrap = 11%

Input = 613.30 units

Scrap = 67.463 units (613.30 units x 11%)

Scrap value = $ 674.63

(67.463 units x $10)

Step 2

Scrap = 9%

Input = 545.837 units (613.30 units – 67.463 units)

Scrap = 49.125 units (545.837 units x 9%)

Scrap value = $ 491.25

(49.125 units x $10)

Step 3

Scrap = 9%

Input = 496.712 units (545.837 units – 49.125 units)

Scrap = 44.704 units (496.712 units x 9%)

Scrap value = $ 447.04

(44.704 units x $10)

Thus scrap value at cost of $10 per unit will cost the company per day at the original scrap rate = $ 1,612.92 rounded off $ 1,613

($ 674.63 + $ 491.25 + $ 447.04)

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