Question

A production process consists of a three-step operation. The scrap rate is 15 percent for the first step and 11 percent for the other two steps. a.lf the desired daily output is 460 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.lf 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

Answer 1

a.

Let the number of start be X.

Then after first step we have (1-0.15)*X = 0.85X

After the second step we have (1-0.11)*0.85X = 0.7565X

After the third step we have (1-0.11)*0.7565X = 0.673285X

If the final output desired is 460 units, then the start should be

460 = 0.673285X

Or X = 683.21 or 684 units (rounding to next whole number)

b.

If the scrap rates are halved then the final output for a start of X will be

(1-0.15/2)*(1-0.11/2)*(1-0.11/2)X

This means in order to get 460 units we need

460/(1-0.15/2)*(1-0.11/2)*(1-0.11/2) = X

X = 556.86 or 557 units

The saving is 684-557 = 127

It will save 127 units

C

In the original part we are scrapping 684-460 = 224 units. The cost is 224*10 = 2240

The cost is 2240