Question

A local grocery store buys USDA A grade pork at the wholesale price of $4 per pound and sells at the retail price of $7 per pound. The grocery store orders once per week. There is no chance to reorder during the week. The meat is good to be sold for one week. Unsold meat have to be dumped (Throw away to regular trash bin is not acceptable, it is hazardous material) at the cost of $0.5 per pound. The weekly demand is uncertain and has a discrete distribution:______.

Demand Probability 300 0.25 400 0.25 500 0.25 600 0.254
How many pounds of meat should be order per week? What is the expected weekly profit?

Answer 1

$1,012.5

Step-by-step explanation:

Cu = Retail price - Wholesale price = $7 - $4 = $3

Co = Wholesale price + Dumping cost = $4 + $0.5 = $4.5

Critical ratio = Cu/(Cu+Co) = 3/(3+4.5) = 0.4

Demand Probability Cumulative probability

300 0.25 0.25

400 0.25 0.50

500 0.25 0.75

600 0.25 1.00

Corresponding demand is 400. Optimal order quantity = 400 pounds

Expected demand = 300*0.25+400*0.25+500*0.25+600*0.25

Expected demand = 450 pounds

Expected shortage = (500-400)*0.25+(600-400)*0.25

Expected shortage = 75

Expected sales = Expected demand - Expected shortage

Expected sales = 450 - 75

Expected sales = 375 pounds

Expected inventory = Order quantity - Expected sales

Expected inventory = 400 - 375

Expected inventory = 25 pounds

Expected weekly profit = Expected sales * Cu - Expected inventory * Co

Expected weekly profit = 375*3 - 25*4.5

Expected weekly profit = $1,012.5