Question

A production process consists of a three-step operation. The scrap rate is 19 percent for the first step and 7 percent for the other two steps.

a.If the desired daily output is 455 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           $  

Answer 1

Here, given that scrape rate is 19% for first step and 7% for other two steps,

Let me consider there are 1000 units,

So, after first step we will get =(1000*(100-19)%)=810 units

After second step, we will get=(810*(100-7)%)=753.3units

After third step, we will get=(753.3*(100-7)%)=700.57 units

a)

Daily desired outputs are 455 units

455*(1000/700.57)=649.47=650 units

We should start with 650 units to allow for loss due to scrape

b)

Scrape rate for each step has become half

Let me consider there are 1000 units,

So, after first step we will get =(1000*(100-9.5)%)=905

After second step, we will get=(905*(100-3.5)%)=873.33

After third step, we will get=(873.33*(100-3.5)%)=842.7635

455*(1000/842.7635)=539.89=540

Now, we should start with 540 units to allow for loss due to scrape

Number of units get saved now=650-540=110

c)

Costing for original company per day for the original scrape rate=(650-455)*10=1950