Question

Cynthia​ Knott's oyster bar buys fresh Louisiana oysters for ​$4 per pound and sells them for ​$10 per pound. Any oysters not sold that day are sold to her​ cousin, who has a nearby grocery​ store, for ​$3 per pound. Cynthia believes that demand follows the normal​ distribution, with a mean of 100 pounds and a standard deviation of 17 pounds. How many pounds should she order each​ day? Refer to the standard normal table for​ z-values.

The table below shows the total area under the normal curve for a point that is Z standard deviations to the right of the mean.

Cynthia should order _____ pounds of oysters each day ​(round your response to one decimal​ place).

Answer 1

ans)

the selling price p=$10 per pound,

the unit cost c=$4 per pound

the salvage value g=$3 per pound

overage cost Co=c−g=4-3=$1

unit underage cost Cu=p−c=10-4=$6

Let F(⋅)denote the cumulative probability function ,

F(Q)>=Cu/(Cu+Co)=0.8571

z value for a cumulative probability of 0.8571 is about 1.06

The optimal order quantity = 100 + 1.06 × 17 ≈ 118.02 pounds

Cynthia should order 118.02 pounds of oysters each day.

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