Question

Suppose you want to sell pumpkins as a fundraiser. You can buy pumpkins from a local farmer for $0.85 each and sell them for $2 apiece. The extra pumpkins left over can only be smashed in celebration and therefore have no salvage value. Assume that the demand for pumpkins during the selling season is normally distributed with a mean of 300 and a standard deviation of 35

• Determine the optimal order quantity for pumpkins that maximizes your expected profit.

• What is your maximum expected profit if you purchase the optimal order quantity?

(IN EXCEL)

Answer 1

	Selling price	$2.00
	Unit cost	$0.85
	Salvage value	$0.00
	Mean demand	300
	Stdev	35
	Underage cost, Cu	$1.15
	Overage cost, Co	$0.85
	Optimum service level, F(z)	0.575
	z	0.189
(a)	Optimum order qty, Q	307
	Loss function, L(z)	0.311
	Expected lost sales, L(Q)	10.90
	Expected sales, S(Q)	289.10
	Expected left-over, V(Q)	17.90
(b)	Expected Profit = S(Q)*Cu - V(Q)*Co	$317.25

Calculations: