Question

Martin Stevens, the manager of a downtown stationary shop must decide how many cartons of Valentines cards to order for the 2019 holiday. Martin has estimated demand will be 40, 80, or 120   cartons and has to decide whether to order 40, 80, or 120 cartons from his supplier. Each carton costs the shop $4.25 and will be sold for $10.00. Any unsold cartons will be sent back to the supplier and Martin will receive a $2.00 refund for each carton that he returns to the supplier.

Past sales and some additional research have given the following probability estimates for demand levels:

40 cartons, 0.30; 80 cartons, 0.40; 120 cartons, 0..30.

a. Construct a payoff table for this problem (alternatives matching the demand levels.)

b. Calculate the Expected Value for each alternative.

c. Based on your calculations, how many cartons of cards should Martin order from his supplier?

Answer 1

(a)	Order	Demand	Sold	Cost	Revenue	Returned	Returned Revenue	Total Revenue	Payoff
	40	40	40	170	400	0	0	400	230
	40	80	40	170	400	0	0	400	230
	40	120	40	170	400	0	0	400	230
	80	40	40	340	400	40	80	480	140
	80	80	80	340	800	0	0	800	460
	80	120	80	340	800	0	0	800	460
	120	40	40	510	400	80	160	560	50
	120	80	80	510	800	40	80	880	370
	120	120	120	510	1200	0	0	1200	690

			States of Nature (Demand)
		40	80	120
Alternatives (Ordered)	40	$230.00	$230.00	$230.00
	80	$140.00	$460.00	$460.00
	120	$50.00	$370.00	$690.00
	Probabilities	0.3	0.4	0.3

(c) Martin should order 120 cards from his supplier.