Susan sells snow cones from a pushcart. Snow cones come in two flavors, Redeye Raspberry (RR) and Boozy Banana (BB). Susan's cost for each cone is the same, $0.50/unit, and she charges $2.00/unit for cones of either flavor. From experience, Susan knows that the daily demand for RR cones is normally distributed with mean 100 and standard deviation 30, while demand for BB cones is normally distributed with mean 120 and standard deviation 60.
Assume that the demand for RR cones is independent of the demand for BB cones (and vice versa), and that demand in excess of supply is lost (no substitutions). Leftover snow cones are discarded at the end of the day.
a. How many RR and BB cones should be stocked at the beginning of the day to maximize Susan's expected profit? What is the expected profit of this policy?
If Susan order too few snow cones of RR, RR shortage cost Cu = Sale price - Purchase price = 2 - 0.50 = $1.50
If Susan Orders too many RR, RR overage cost Co = 0.50
So Critical ratio F(Q) = ?Cu/(Co+Cu) = 1.50 / (1.50+0.50) = 0.75
We find from Normal table that for Probability = 0.75, z = NORM.S.INV(0.75) = 0.6745
So Optimal Qty of RR cones Susan should stock Q = Mean + z*Std Dev = 100 + 0.6745*30 = 121 Cones
Similarly Optimal Qty of BB cones Susan should stock Q = Mean + z*Std Dev = 120 + 0.6745*60 = 161 Cones
Number of RR Cones 121 Cones
Number of BB Cones 161 cones
Expected Profit = Cu*(RR+BB) = 1.50*(121+161) = $423
b. If Susan can stock no more than 250 snow cones, how many RR and BB cones should be stocked at the beginning of the day to maximize Susan's expected profit? What is the expected profit of this policy (Hint: the maximum order size makes the cost of overstocking cones of either flavor increase)?
Number of RR Cones ____________
Number of BB Cones ____________
Expected Profit ____________