Question

A production process consist of a three-step operation. The scrap rate is 16% for the first step and 10% for the other two steps

a. if they desire daily output is 496 units, how many units must be started to allow for the loss due to the scrap? Do not round intermediate calculations round up your final answer to the next whole number

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 scrap allowance? do not round intermediate calculations round your final answer to the next phone number

c. if this graph represents the cost of $10 per unit, how Much is it costing the company per day for the original scrap rate? Round your final answer to the nearest whole number

Answer 1

Answer:

a) 729 units

Assume that at start process has X units.

Output of 1st Step = X - 0.16 X = 0.84 X (16% Scrap)

Output of 1st step is an input to 2nd Step

Output of 2nd Step = 0.84 X - 0.10(0.84 X) = 0.756 X (10% Scrap at 2nd Step)

Output of 2nd step is an input to 3rd Step

Final Output = Output of 3rdStep = 0.756 X - 0.10(0.756 X) = 0.6804 X (10% Scrap at 3rd Step)

Desired Daily Output = 496 units

0.6804 X = 496

X = 728.98 ~ 729 units

Scrap Allowance = 729-496 = 233

b)

Scrap rate cut to half for all steps

Assume that at start process has X units.

Output of 1st Step = X - 0.08 X = 0.92 X (8% Scrap)

Output of 1st step is an input to 2nd Step

Output of 2nd Step = 0.92 X - 0.05(0.92 X) = 0.874 X (5% Scrap at 2nd Step)

Output of 2nd step is an input to 3rd Step

Final Output = Output of 3rdStep = 0.874X - 0.05(0.874 X) = 0.8303 X (5% Scrap at 3rd Step)

Desired Daily Output = 496 units

0.8303 X = 496

X = 597.37 ~ 598 units

Scrap Allowance = 102

Save in scrap allowance = Original Scrap - Scrap amount after cut of scrap rate = 233 - 102 = 131 units

c)

Total Costing to company due to scrap = Scrap allowance * Cost per unit = 233*10 = $2330