Susan sells snow cones from a pushchart. Snow cones come in two flavours, Redeye

Question

Susan sells snow cones from a pushchart. Snow cones come in two flavours, Redeye Raspberry (RR) and Boozy Banana (BB). Susans cost for each cone is the same, $0.50/unit, and she charges $2.00/unit for cones of either flavour. From experience, Susan knows that the daily demand for RR cones is normally distributed with the 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 that demand in excess of supply is lost. 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 Susans expected profit? What is the expected profit of this policy? If susan can stock no more than 250 snow, how many RR and BB cones should be stocked at the beginning of the day to maximize Susans expected profit? What is the expected profit of this policy.

Explanation / Answer

Accordding to the given question we have the following infirmation:

(a)Let us supppose that susan sells X RR snow cones and Y BB snow cones.

So, the profit will be say Z = $1.5X + $1.5Y

then her expecter profit is E(Z) = $1.5E(X) + $1.5E(Y) =$1.5(100) + $1.5(120) = $(150+180) =$330

Total number of cones that she should stock $330/$1.5 = 220

so she need to have atleast 220 snow cones. Since, the demand for these cones are normally distributed we may assume that on any given day the demand for RR snow cones will be E(X)=100 and the demand for BB cones will be E(Y)=120. So, we stick to this and we stock 100 RR snow cones and 120 BB snow cones. i.e 100+120=220 cones.

So, Number of RR cones=100; Number of BB cones=120; Expected profit($)=$330

(b) Here, we are given that X+Y<=250. ket us consider that she chooses to use this limit to the max.

So,let there be X RR snow cones and (250-X) BB snow cones

So, our expected profit in this case Z =$1.5X +$1.5Y = $1.5X + $1.5(250-X)

E(Z) = $1.5E(X) + $1.5(250-E(X)) =$150 + $375 - $150 =$375

So, the expected profit is $375

Redeye Raspberry(RR) Boozy Banana(BB) Cost $0.5 $0.5 Price $2.0 $2.0 Profit $1.5 $1.5 Mean 100 120 S.D 30 60

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