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Elena-2011 [213]
3 years ago
12

A quality inspector for Alpha-Beta Co. is concerned about the quality of the batch of several thousand blank DVD disks which his

company produced this week and is preparing to ship. If the cost of replacing a defective DVD disk once it has been shipped is $2.50, while the cost for 80% inspection prior to shipment is $0.32 each, while the cost of 100% inspection prior to shipment is $0.40 each, at what point is she indifferent between 100% inspection and shipment without inspection?
a. 12.8% defectives
b. 16% defectives
c. 20% defectives
d. 32% defectives
Business
1 answer:
Mazyrski [523]3 years ago
3 0

Answer:

b. 16% defectives

Explanation:

Let the number of units shipped be N

Let the defect rate be y%

Cost of replacing defectives once shipped = (y/100)×N× 2.5  ........equation (1)

Cost of 100% inspection = N × 0.4 .........equation (2)

At the indifference point, both costs, that is the replacement cost and inspection cost are equal. Therefore, we make both equations (1) and (2) equal.

N × 0.4 = (y/100)×N× 2.5

100 × 0.4 = y ×2.5

y = 40/2.5 = 16

She is indifferent at 16% defectives

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Answer:

Products    Selling price   Unit variable cost   Contribution per unit

                        $                           $                             $

M                      7                           3                             4

N                       6                          2                             4

O                       6                          3                             3

                        19                          8                            11

Break-even point in composite units

= <u>Total fixed cost</u>

  Contribution per unit

= <u>$340,000</u>

         $11

= 30,909 units

Break-even point for the current sales mix

M    3/6 x 30,909 units = 15,455 units

N     1/6 x 30,909 units = 5,151 units

O     2/6 x 30,909 units = 10,303 units

Explanation:

In this case, we need to calculate contribution per unit of each product by deducting the unit variable cost of each product from their respective selling prices. Then, we will obtain the break-even point in composite units by dividing the total fixed cost by overall contribution per unit.

Then, we will determine the break-even point for the current sales mix by multiplying the proportion of each product in the sales mix by the break-even point in composite units.

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3 years ago
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