Question

A production process consists of a three-step operation. The scrap rate is 19 percent for the first step and 10 percent for the other two steps.

a.If the desired daily output is 495 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

A. Let X be the original quantity.

The first operation has scrap rate = 19% of original quantity

Scrap = 0.19x

After the first step, quantity remains = original quantity - scrap

= x - 0.19x

= 0.81x

After second operation, scrap of 10%

Scrap = 10% of quantity remaining after operation 1

= 0.10 x 0.81x

=0.081x

Quantity remaining = quantity after operation 1 -scrap

= 0.81x - 0.081x

=0.729x

After third operation, scrap of 10%

Scrap = 10% of quantity remaining after operation 2

Scrap = 0.10 x 0.729x

Scrap = 0.0729x

Quantity remaining = quantity after operation 2 - scrap

= 0.729x - 0.0729x

=0.6561x

Now given that this final quantity remaining is equal to 495 units.

So framing this equation, we get

0.6561x = 495

X = 495/0.6561

X = 754.458

Hence to get 495 units, the original quantity required js 754.48 units or 755 units.

2. The scrap rate is cut in half.

Scrap rate at first operation is = 19/2 = 9.5%

Scrap rate at second and third operation = 10/2 = 5% each

Now let us follow the same process as above.

Let the original quantity be x.

Scrap rate at the end of operation 1 = 9.5% of original quantity.

Scrap rate = 0.095x

Remaining quantity = original quantity - scrap

= x - 0.095x

= 0.905 x

Scrap rate at the end of operation 2 = 5% of quantity remaining after operation 1.

Scrap rate = 0.05 * 0.905x

= 0.04525x

Quantity remaining = Quantity after operation 1 - scrap

= 0.905x - 0.04525x

= 0.85975x

Scrap at the end of operation 3 = 5% of quantity remaining of operation 2

= 0.05 * 0.85975x

= 0.0429875x

Quantity after operation 3 = quantity remaining after operation 2 - scrap

= 0.85975x - 0.0429875x

= 0.8167625x

So the end number of units is given as equal to 495 units.

Or, 0.8167625x = 495

Or, x = 495/0.8149625

X = 606.05 units or 607 units

With the original scrap rate, the units to be introduced were 754 units and now it is 607 units.

Savings in term of scrap allowance = 754 - 607

=147  units.

3. At the original scrap rate, the quantity to be introduced is 754 units.

The quantity remaining after the third operation is 495 units.

Scrap = 754 - 495 = 259 units.

Cost of each unit of scrap = $10

Total scrap cost = 259  x 10 = $2590