Question

The owner of a newsstand wants to determine the number of Canada Post that must be stocked at the start of each day. It costs 30 cents to buy a copy, and the owner sells it for 75 cents. The sale of the newspaper typically occurs between 7:00 and 8: am. Newspapers left at the end of the day are recycled for an income of 5 cents a copy. How many copies should the owner stock every morning in order to minimize the total cost (or maximize the profit), assuming that the demand for the day can be approximated by

• A normal distribution with mean 300 copies and standard deviation 20 copies
• A discrete pdf defined as

• Demand	200	220	300	320	340
  f(D)	0.1	0.2	0.4	0.2	0.1
  F(D)	0.1	0.3	0.7	0.9	1.0

  i need a description for each step not only numbers plz

Answer 1

• Profit for each copy sold is computed here as:
  = SP - CP = 75 - 30 = 45 cents per copy
• Loss from each copy unsold
  = Recycle Value - CP = 5 - 30 = -25

Let us calculated the expected profit for each stock value here as:

• For Stock = 200,
  E(Profit) = E(Profit when all 200 would be sold)
  E(Profit) = 200*45 = 9000 Cents
• For Stock = 220
  E(Profit) = 0.1*(9000 - 25*20) + 0.9*220*45 = 850 + 8910 = 9760
• For stock = 300,
  E(Profit) = 0.1*(9000 - 100*25) + 0.2*(220*45 - 80*25) + 0.7*300*45 = 650 + 1580 + 9450 = 11680
• For stock = 320,
  E(Profit) = 0.1*(9000 - 120*25) + 0.2*(220*45 - 100*25) + 0.4*(300*45 - 20*25) + 0.3*320*45
  = 600 + 1480 + 5200 + 4320
  = 11600 < 11680

Therefore to minimize the cost, 300 copies should be stocked every morning in order to minimize the total cost