Problem 10-18 A production process consists of a three-step operation. The scrap

Question

Problem 10-18 A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 percent for the other two steps. a. If the desired daily output is 450 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 $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your answer to the nearest whole number. Omit the "$" sign in your response.) Cost

Explanation / Answer

Given values:

A three-step process

Scrap rate at step-1 = 10% = 0.10

Scrap rate at step-2 = 6% = 0.06

Scrap rate at step-3 = 6% = 0.06

Solution:

(a) Let the starting quantity be denoted by symbol Sq.

Starting quantity = Sq units

Scrap rate at step-1 = 10% = 0.10

Quantity left after step-1 = Sq - (0.10 x Sq) = (0.90) Sq

Scrap rate at step-2 = 6% = 0.06

Quantity left after step-2 = (0.90) Sq - (0.90 Sq x 0.06) = 0.846 Sq

Scrap rate at step-3 = 6% = 0.06

Quantity left after step-3 = (0.846) Sq - (0.846 Sq x 0.06) = 0.795 Sq

Desired daily output = 450 units

That means,

0.795 Sq = 450

Starting quantity, Sq = 566.04 or 566 units

If the desired daily output is 450 units, the starting quantity must be 566 units to allow for loss due to scrap.

(b) If the scrap rate for each step could be cut in half at every operation, the new scrap rates are as follow:

Scrap rate at step-1 = 5% = 0.05

Scrap rate at step-2 = 3% = 0.03

Scrap rate at step-3 = 3% = 0.03

Let the starting quantity be denoted by symbol Sq.

Starting quantity = Sq units

Scrap rate at step-1 = 5% = 0.05

Quantity left after step-1 = Sq - (0.05 x Sq) = (0.95) Sq

Scrap rate at step-2 = 3% = 0.03

Quantity left after step-2 = (0.95) Sq - (0.95 Sq x 0.03) = 0.9215 Sq

Scrap rate at step-3 = 3% = 0.03

Quantity left after step-3 = (0.9215) Sq - (0.9215 Sq x 0.03) = 0.893855 Sq

Desired daily output = 450 units

That means,

0.893855 Sq = 450

Starting quantity, Sq = 503.44 or 504 units

Number of units saved = Original quantity - New quantity

Number of units saved = 566 - 504

Number of units saved = 62 units

(c) Scrap costs = $10 per unit

Total scrap cost = Total scrap x Scrap cost per unit

Total scrap cost = (Input - Output) x Scrap cost per unit

Total scrap cost = (566 - 450) x 10

Total scrap cost = $1,160

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