Question

consider a product meeting the newsvendor assumptions. The unit purchase cost is $140. For each sold unit, you earn a profit of $60. For each leftover, you lose $30. The demand follows a normal distribution with a mean 80 and a standard deviation 30. Calculate the newsvendor critical ratio. what is the optimal order quantity

Answer 1

Newsvendor critical ratio = 0.35

Optimal quantity = 92.6 units

Step-by-step explanation:

Cost = $140

Profit = $60

Loss =$30

Mean = 80

S.D = 30

Revenue = cost + profit

= 140 +60

= $200

Cost of under stock = revenue - cost

= 200 - 140

= $60

Cost of over stock = cost - salvage value

= 140 - 30

= $110

The newsvendor critical ratio is calculated using the formula;

newsvendor critical ratio=

Cost of under stock/Cost of under stock + Cost of over stock

Newsvendor critical ratio= 60/(60+ 110)

= 60/170

= 0.35

z = 0.3853

Optical quantity is given as;

Q = 80 + 0.3853* 30

= 92.6 units