a production process consists of a three consists of a three-step operation. The

Question

a production process consists of a three consists of a three-step operation. The scrap rate is 16 percent for the first step and 8 percent for the other two A production process steps olf the desired daily output is 457 units, how many units must be started to allow for loss due to scrap? (Do not round intermediate Number of unitsN calculations. Round up your final answer to the next whole number.) b.lf the scrap rate for each st allowa ep could be cut in half at every operation, how many units would this save in terms of the scrap nce? (Do not round intermediate calculations. Round up your final answer to the next whole n Number of units e scrap represents a cost of S10 per unit, how much is it costing the company per day for the original scrap rate (Le, the Part a scrap rate)? (Round your final answer to the nearest whole number. Omit the "$" sign in your response.) Cost

Explanation / Answer

Scrap rate is the rate of defective outputs. A scrap rate of 16 percent means if we start with 100 units, the final product count will be 100-16 = 84 units.

a. Let’s take the initial number of units to be X. After the process 1, the number of units that will qualify is 0.84X. When 0.84X units go into the process 2, the output will be 0.92*0.84X units. When these units go through process 3, the output will be 0.92*0.92*0.84X units.

If the value X satisfies the final output of 457 units then we can equate it as

0.92*0.92*0.84X = 457

0.710976X = 457

X = 457 / 0.710976 = 642.7783

Rounding up the value we have 643 units

b. If the scrap rates were halved then the equation will be modified as

0.96*0.96*0.92X = 457

X = 457 / 0.8478 = 538.99 or 539 (rounding up).

The number of units this saves is 643 – 539 = 104 units

104 units will be saved

c. The original scrap allowance is 643 – 457 = 186.

With a cost of $10 per unit the cost to the company is 186*10 = 1860

The cost is $1860

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