Question

A production process consists of a three-step operation. The scrap rate is 16 percent for the first step and 11 percent for the other two steps. a.If the desired daily output is 494 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 $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Parta scrap rate)? (Round your final answer to the nearest whole number. Omit the "$" sign in your response.) Cost

Answer 1

(a)

Let X be the startup units

Please note that material left in one process is used as raw material for the next process and so on . Material left in step 3 will be the final out put

	Setp-1	Setup-2	Setup-3
Scrap rate(%)	16	11	11
Units Scraped	x*16/100= 0.16 x	0.84x *11/100=0.092x	0.75x *11/100=0.083
Left material	x-0.16x =0.84 x	0.84x -0.092x=0.75x	0.75x-0.083 x =0.667 x

Given that Final output = 494 Units

Therefore 0.667 X = 494 ; X = 494/0.667 = 740.6 ( Round figure 741)

(b)

Total scrap allowence in (a) = 0.16x + 0.092x  + 0.083x  = 0.335* 741 = 0.335 = 247 .9 units (248 round figure)

If the values of scrap generation be half the table will be as follows

	Setp-1	Setup-2	Setup-3
Scrap rate(%)	8	5.5	5.5
Units Scraped	x*8/100= 0.08 x	0.92x *5.5/100=0.050x	0.87x *5.5/100=0.048x
Left material	x-0.08x =0.92 x	0.92x -0.050x=0.87x	0.87x - 0.048 x =0.822 x

Scrap Allowance = 0.08x + 0.05x + 0.048 x = 0.178* 741 = 131.89 (132 round figure)

Saving in the scrap Units = 248 -132 = 116

(c)

Cost of scrap =$ 10 unit

Total cost of scrap in (a) per day = $ 248 * 10 =$ 2480