Question

Produce Company needs to know the pounds of bananas to have on hand each day. Each pound of bananas costs $0.10 and can be sold for $0.30. Unsold bananas are worthless at the end of the day. The following demands were found after studying the last six months' sales:

300 pounds of bananas 25% of the time

400 pounds of bananas 40% of the time

500 pounds of bananas 35% of the time

Required: Determine whether Produce Company should order 300, 400, or 500 pounds of bananas. Show your work.

Answer 1

Quantity Ordered	Demand Probability			Expected Value
	300	400	500
300	60	60	60	$60
400	50	80	80	$72.50
500	40	70	100	$73.00
Probability	25%	40%	35%

Demand probability

300 pounds of bananas

(300*0.20) = 60

400 pounds of bananas

(300*0.20)-(100*0.10) = 50

(400*0.20) = 80

500 pounds of bananas

(300*0.20)-(200*0.10) = 40

(400*0.20)-(100*0.10) = 70

(500*0.20) = 100

Expected value

300 pounds of bananas = (25%*60)+(40%*60)+(35%*60) = $60

400 pounds of bananas = (25%*50)+(40%*80)+(35%*80) = $72.5

500 pounds of bananas = (25%*40)+(40%*70)+(35%*100) = $73.00

The expected value is higher in case of 500 pounds of bananas, thus Produce Company should order 500 pounds of bananas to maximize profit.