Answer:
Explanation:
(a) The cost of underage(Cu) will be the opportunity cost for lost sales which will be:
= 65 - 40
= 25
The cost of overage(Co) will be the holding cost which will be:
= 40 x 35%/52
= 40 × 0.35/52
= 40 × 0.0067308
= 0.269
The Critical ratio will be:
= Cu/(Cu + Co)
= 25/(0.269+25)
= 0.9894
For the optimal condition,
F(z) = Critical ratio = 0.9894,
therefore, z = normsinv (0.9894) = 2.30
Therefore, the optimal stock will be calculated as:
= Mean demand + (z × Stdev)
= 35 + (2.30 × 10)
= 35 + 23
= 58 units.
We should note that Tammi already has 12 cushions in stock, therefore the order quantity will be:
= 58 - 12
= 46 units
(b) Cu = 12
Co = 0.269
Critical ratio will be:
= Cu/(Co + Cu)
= 12 / (12 + 0.269)
= 0.9781
Therefore, z = normsinv(0.9781) = 2.0
Then, the optimal stock will be:
= 35 + (2.0 × 10)
= 35+20
= 55 units
We should note that Tammi already has 12 cushions in stock, therefore the order quantity will be:
= 55 - 12
= 43 units
