Cynthia Knott\'s oyster bar buys fresh Louisiana oysters for $5 per pound and se

Question

Cynthia Knott's oyster bar buys fresh Louisiana oysters for $5 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 120 pounds and a standard deviation of 11 pounds. How many pounds should she order each day? Refer to the standard normal table

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

Explanation / Answer

Purchase cost = $5 per pound

Selling price = $10 per pound

Salvage value = $3 per pound

Mean demand = µ =120 pounds

Standard Deviation = = 11 pounds

For the given data apply single-period Inventory model

Cs = cost of shortage (underestimate demand) = Sales price/unit – Cost/unit

Co = Cost of overage (overestimate demand) = Cost/unit – Salvage value /unit

Cs = 10 – 5 = $5 per pound

Co = 10 – 3 = $7 per pound

The service level or probability of not stocking out, is set at,

Service Level = P(demand <= Q*) = Cs/( Cs + Co) = 5/(5+7) = 5/12

Service Level = 0.4167

Cynthia needs to find the Z socre for the demand normal distribution that yields a probability of 0.416.

So 41.67% of the area under the normal curve must be to the right of the optimal stocking level.

Using standard normal table, for an area of 0.4167, the Z score is -0.21.

Optimal order quantity = µ + z = 120 + (-0.21)11

Optimal order quantity = 117.69 pounds or 118 pounds

Cynthia should order 118 pounds of oysters each day.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.