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 13 percent for the first step and 7 percent for the other two steps.

a.If the desired daily output is 475 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

Scrap rate of step 1 = 13%, therefore efficiency is 87%

Similarly, efficiency of step 2 and 3 are (100-7) = 93%

a) Now, input = output/ efficiency and input of a step = output of previous step

Output of step 3 = 475

therefore, input of step 3 = output of step 2 = 475/0.93 = 510.75

therefore, input of step 2 = output of step 1 = 510.75/.93 = 549.146

therefore input of step 1 = 549.146/0.87 = 631.26

~632 units must be started with

b) If scrap rate is cut into half, scrap rates of step 1,2 and 3 are 6.5%, 3.5% and 3.5% respectively.

Accordingly, efficiencies are 93.5%, 96.5% and 96.5% respectively

Therefore, inputs required are ((475 / 0.965) / 0.965) / 0.935 = 545.54

~ 546 units are required.

Therefore, savings in scrap = 632-546 = 86 units

c) Total units input = 632

Total output = 475

Scrappage = 632 - 475 = 157 units

Therefore, cost of scrap at the rate of $10 per unit = $ 10* 157 = $1570 per day

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