Question

Cynthia​ Knott's oyster bar buys fresh Louisiana oysters for ​$4 per pound and sells them for ​$8 per pound. Any oysters not sold that day are sold to her​ cousin, who has a nearby grocery​ store, for ​$2 per pound. Cynthia believes that demand follows the normal​ distribution, with a mean of 120 pounds and a standard deviation of 18 pounds. How many pounds should she order each​ day?

Answer 1

128 pounds

Step-by-step explanation:

Cost of buying of Louisiana oysters = $4 per pound

Cost of selling of Louisiana oysters = $8 per pound

selling cost of oysters not sold = $2

Mean = 120 pounds

Standard deviation, s = 18 pounds

Thus,

Cost of actual Utilization (Co) = $8 - $4 = $4

Cost of Under utilization (Cu) = $4 - $2 = $2

Now,

Probability of sale =
`\frac{\textup{Co}}{\textup{(Cu+Co)}}`

=
`\frac{\textup{4}}{\textup{(2+4)}}`

= 0.67

also,

z score at above probability (0.67) = 0.44 [from standard z-table]

hence,

Cynthia should order = mean + z × s

= 120 + 0.44 × 18

= 120 + 7.92

= 127.92 ≈ 128 pounds