Question

cynthia​ Knott's oyster bar buys fresh Louisiana oysters for ​$55 per pound and sells them for ​$1010 per pound. Any oysters not sold that day are sold to her​ cousin, who has a nearby grocery​ store, for ​$33 per pound. Cynthia believes that demand follows the normal​ distribution, with a mean of 120120 pounds and a standard deviation of 1111 pounds. How many pounds should she order each​ day

Answer 1

Given Information:

Cost price of oysters = $5 per pound

Selling price of oysters = $10 per pound

Salvage value = $3 per pound

Mean demand of oysters = μ = 120 pounds

Standard deviation = σ = 11 pounds

Required Information:

How many pounds of oysters should she order each​ day = ?

Answer:

She should order 126 pounds of oysters each day

Explanation:

The required pounds of oysters that cynthia​ should order is given by

n = μ + zσ

Where μ is the mean demand of oysters, σ is the standard deviation, and z is calculated by

p = C_us/(C_us + C_os)

Where

C_us is the cost of under utilization

C_os is the cost of actual utilization

C_us = Selling price - Cost price

C_us = $10 - $5

C_us = $5

C_os = Cost price - Salvage value

C_os = $5 - $3

C_os = $2

p = C_us/(C_us + C_os)

p = 5/(5 + 2)

p ≈ 71%

The z-score corresponding to 71 percentile is 0.553

n = 120 + (0.553)11

n = 120 + 6.083

n = 126 pounds

Therefore, cynthia​ should buy 126 pounds of oysters each day