Question

For our online store for gadgets from Session 8 HW, we know that one new product’s demand is normally distributed with an expected mean demand for the season of 300 and a standard deviation of 300. The product sells for $100, the cost of the product is $50, and the salvage is $20. We have now, however, a second supplier, which is more expensive, but which is very close and can provide a second order with a short lead time after the beginning of the season (Reactive Capacity). The cost of the product for this supplier is $60.

a. What is the cost of underage and the cost of overage for the gadget store with this second supplier?

Cu = c2 – c1 (this is the “premium” the online store pays for the second order vs. the first order)

Co = c1 – v (no change)

Select one:

a) Cu = $50, Co = $30

b) Cu = $10, Co = $20

c) Cu = $10, Co = $30

b. What is now the optimal order quantity for the gadget store with the second supplier?

Hint: Critical Ratio = Cu/(Cu + Co). In this case the critical ratio = 0.2500.

Then look up the corresponding z value and convert to Q *= μ + zσ

Select one:

a) 99

b) 150

c) 396

d) 410

Answer 1

Answer: - According to given data

Mean demand = 300 and Standard deviation = 300

a) Option"C" --- Cu = $10, Co = $30

Supplier 2: Selling price = $60, Cost price = $50 and Salvage = $20

Formula to calculate Cu and Co is

Underage cost = Selling price - Cost price = $60 - $50 = $10

Overage cost = Cost price - Salvage = $50 - $20 = $30

b) Option"A" --- 99

Critical value = Cu / (Cu + Co ) = $10 / $40 = 0.2500

The z value for the obtained critical value = -0.67

Q = Mue + Z * Standard deviation

Q = 300 + (-0.67)*300 = 300 - 201 = 99