A production process at Firsten Last, Inc. has two in-line stages. The probabili

Question

A production process at Firsten Last, Inc. has two in-line stages. The probability of defects occurring ini stage 1 is 30%. If there is a defect at stage 1, there is a 90% chance of defect at stage 2. If there is no defect at stage 1, the probability of a defect at stage 2 is 20%. Finished units that only have a stage 1 defect can be repaired at a cost of $7. A stage 2 only defect costs $11 to repair. Items with a stage 1 and a stage 2 defect must be scrapped at a cost of $2 each.    It costs $18 to manufacture and $5 to test each unity. The shipping cost is $3 per unit. They sell for $50 each.    a.) what percentage of finished units will have the folloiwng attributes? i.) no defects, ii.) a stage 1 defect only iii.) a stage 2 defect only, and iv.) a stage 1 and a stage 2 defect    b.) what is the expected profit per unit?

Explanation / Answer

I ) Percentage of finished units with no defects

= Percentage of units with no defects at stage 1 x Percentage of units with no defects at stage 2 if there is no defect at stage 1

= ( 100 % - 30% ) x ( 100% - 20%)

= 70% of 80%

= 56 %

ii) Percentage of finished unit with stage 1 defect ONLY

= Percentage of units with defects at stage 1 x Percentage of units with no defect at stage 2 if there is a defect at stage 1

= 30 % x ( 100% - 90%)

= 30% of 10%

= 3 %

iii)Percentage of finished units with Stage 2 defect only

= Percentage of units with no defects at stage 1 x Percentage of units with defects at stage 2

= ( 100 % - 30% ) x 20%

= 70% of 20%

= 14%

iv)Percentage of units with stage 1 as well as stage 2 defect

= Percentage of units with stage 1 defect x Percentage of units with stage 2 defects

= 30% of 90%

= 27%

= Percentage of stage 1 defect only /100 x $ 7 repair cost per unit + Percentage of stage 2 defect only/100 x $11 repair cost per unit + Percentage of stage 1 as well as stage 2 defect/100 x $2 scrapping cost per unit

= 0.03 x $7 + 0.14 x $11 + 0.27 x $2

= $0.21 + $1.54 + $0.54

= $2.29

Expected profit per unit

= Sale price /unit – Manufacturing cost/ unit – Testing cost /unit – Shipping cost /unit – Expected repair cost / unit

= 50 – 18 – 5 – 3 – 2.29

= $21.71

EXPECTED PROFIT PER UNIT = $21.71 PER UNIT

EXPECTED PROFIT PER UNIT = $21.71 PER UNIT

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