Question

In: Statistics and Probability

Cynthia​ Knott's oyster bar buys fresh Louisiana oysters for ​$4 per pound and sells them for...

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 10 pounds. How many pounds should she order each​ day? Refer to the standard normal table for​ z-values.

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

Z

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0

0.5000

0.5040

0.5080

0.5120

0.5160

0.5199

0.5239

0.5279

0.5319

0.5359

0.1

0.5398

0.5438

0.5478

0.5517

0.5557

0.5596

0.5636

0.5675

0.5714

0.5754

0.2

0.5793

0.5832

0.5871

0.5910

0.5948

0.5987

0.6026

0.6064

0.6103

0.6141

0.3

0.6179

0.6217

0.6255

0.6293

0.6331

0.6368

0.6406

0.6443

0.6480

0.6517

0.4

0.6554

0.6591

0.6628

0.6664

0.6700

0.6736

0.6772

0.6808

0.6844

0.6879

0.5

0.6915

0.6950

0.6985

0.7019

0.7054

0.7088

0.7123

0.7157

0.7190

0.7224

0.6

0.7258

0.7291

0.7324

0.7357

0.7389

0.7422

0.7454

0.7486

0.7518

0.7549

0.7

0.7580

0.7612

0.7642

0.7673

0.7704

0.7734

0.7764

0.7794

0.7823

0.7852

0.8

0.7881

0.7910

0.7939

0.7967

0.7996

0.8023

0.8051

0.8079

0.8106

0.8133

0.9

0.8159

0.8186

0.8212

0.8238

0.8264

0.8289

0.8315

0.8340

0.8365

0.8389

1.0

0.8413

0.8438

0.8461

0.8485

0.8508

0.8531

0.8554

0.8577

0.8599

0.8621

1.1

0.8643

0.8665

0.8686

0.8708

0.8729

0.8749

0.8770

0.8790

0.8810

0.8830

1.2

0.8849

0.8869

0.8888

0.8907

0.8925

0.8944

0.8962

0.8980

0.8997

0.9015

1.3

0.9032

0.9049

0.9066

0.9082

0.9099

0.9115

0.9131

0.9147

0.9162

0.9177

1.4

0.9192

0.9207

0.9222

0.9236

0.9251

0.9265

0.9279

0.9292

0.9306

0.9319

1.5

0.9332

0.9345

0.9357

0.9370

0.9382

0.9394

0.9406

0.9418

0.9430

0.9441

1.6

0.9452

0.9463

0.9474

0.9485

0.9495

0.9505

0.9515

0.9525

0.9535

0.9545

1.7

0.9554

0.9564

0.9573

0.9582

0.9591

0.9599

0.9608

0.9616

0.9625

0.9633

1.8

0.9641

0.9649

0.9656

0.9664

0.9671

0.9678

0.9686

0.9693

0.9700

0.9706

1.9

0.9713

0.9719

0.9726

0.9732

0.9738

0.9744

0.9750

0.9756

0.9762

0.9767

2.0

0.9773

0.9778

0.9783

0.9788

0.9793

0.9798

0.9803

0.9808

0.9812

0.9817

2.1

0.9821

0.9826

0.9830

0.9834

0.9838

0.9842

0.9846

0.9850

0.9854

0.9857

2.2

0.9861

0.9865

0.9868

0.9871

0.9875

0.9878

0.9881

0.9884

0.9887

0.9890

2.3

0.9893

0.9896

0.9898

0.9901

0.9904

0.9906

0.9909

0.9911

0.9913

0.9916

2.4

0.9918

0.9920

0.9922

0.9925

0.9927

0.9929

0.9931

0.9932

0.9934

0.9936

2.5

0.9938

0.9940

0.9941

0.9943

0.9945

0.9946

0.9948

0.9949

0.9951

0.9952

2.6

0.9953

0.9955

0.9956

0.9957

0.9959

0.9960

0.9961

0.9962

0.9963

0.9964

2.7

0.9965

0.9966

0.9967

0.9968

0.9969

0.9970

0.9971

0.9972

0.9973

0.9974

2.8

0.9974

0.9975

0.9976

0.9977

0.9977

0.9978

0.9979

0.9980

0.9980

0.9981

2.9

0.9981

0.9982

0.9983

0.9983

0.9984

0.9984

0.9985

0.9985

0.9986

0.9986

3.0

0.9987

0.9987

0.9987

0.9988

0.9988

0.9989

0.9990

0.9989

0.9990

0.9990

Solutions

Expert Solution

Data given for Knott’s oyster bar

Purchase cost = C = $4 per lb

Selling price = P = $8 per lb

Salvage value = S = $2.00 per lb

Mean demand = µ = 120 lb

Standard Deviation = σ = 10 lb

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 = 8 – 4 = $4 per lb

Co = 4 – 2 = $2 per lb

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

Service Level = Cs/( Cs + Co) = 4/(4 + 2)

Service Level = 0.6667

Cynthia needs to find the Z socre for the demand normal distribution that yields a probability of 0.6667

So 66.67% 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 0.6667, the Z score is 0.7454

Optimal order quantity = µ + zσ = 120 + (0.7454)10 = 120.74 lb

Optimal order quantity = 120

Cynthia should order 120 lb of oyster to maximize the revenue.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

7) Skinner’s Fish Market buys fresh Boston bluefish daily for $4.20 per pound and sells it...
7) Skinner’s Fish Market buys fresh Boston bluefish daily for $4.20 per pound and sells it for $5.70 per pound. At the end of each business day, any remaining bluefish is sold to a producer of cat food for $2.40 per pound. Daily demand can be approximated by a normal distribution with a mean of 47 pounds and a standard deviation of 16 pounds. What is the optimal stocking level? Round your answer to 2 decimal places.
The Islander Fishing Company purchases clams for K1.50 per pound from fishermen and sells them to...
The Islander Fishing Company purchases clams for K1.50 per pound from fishermen and sells them to various restaurants for K2.50 per pound. Any clams not sold to the restaurants by the end of the week can be sold to a local soup company for K0.50 per pound. The company can purchase 500, 1,000, or 2,000 pounds. The probabilities of various levels of demand are as follows: Demand (Pounds) Probability 500 1,000 2,000 0.2 0.4 0.4 (a)          For each possible purchase...
A supplier to a music store buys compact discs at $1 per unit and sells them...
A supplier to a music store buys compact discs at $1 per unit and sells them to the music store at $5 per unit. The music store sells each disc to the end consumer at $10. At the retail price, the market demand distribution is give as follows Demand Prob. 1 0.15 2 0.20 3 0.35 4 0.30 With no contract in place, determine how much the music store should order to maximize it’s expected profit? (8 points) (4 points)...
A saleswoman sells a? dried-fruit mixture for ?$5.90 per pound and nuts for ?$14.55 per pound....
A saleswoman sells a? dried-fruit mixture for ?$5.90 per pound and nuts for ?$14.55 per pound. She wants to blend the two to get a 10?-lb mixture that she will sell for ?$9.36 per pound. How much of each should she? use? Solve using matrices.
A company sells ”sports sets” that consist of one bar, two 20-pound weights, and four 5-pound...
A company sells ”sports sets” that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pound. The weights average the specified amounts, but the standard deviations are 0.2 pound for the 20-pounders and 0.1 pound for the 5-pounders. We can assume that all the weights are normally distributed. a. The company ships each set to customers in two different containers: The bar is shipped...
Question 6 The Sock company buys hiking socks for GHS6 per pair and sells them GHS10....
Question 6 The Sock company buys hiking socks for GHS6 per pair and sells them GHS10. Management budgets monthly fixed costs of GHS12,000 for sales volume between 0 and 12,000 pairs. Required Consider the following questions separately by using the foregoing information each time. i. Calculate the breakeven point in units. ii. The Sock Company reduces its sales price from GHS10 per pair to GHS8 per pair. Calculate the new breakeven point in units. iii. The Sock Company finds a...
Mimova Ltd buys shoes from a supplier in France and sells them on to retailers in...
Mimova Ltd buys shoes from a supplier in France and sells them on to retailers in Australia. Mimova Ltd currently uses an EOQ model to determine the number of shoes to send to order. Annual demand for shoes are approximately 45,600. The ordering cost is $55 per order. The annual cost of physically storing shoes is $8.75 per unit. The insurance on the inventory (shoes) cost is $4.25 per unit. The opportunity cost (annual ROI 25% x $30) is $7.50...
a coffee shop buys beans 3.2$ per bag, and it sells it for 5.25 $. this...
a coffee shop buys beans 3.2$ per bag, and it sells it for 5.25 $. this coffee shop sales are 21 bag per week. its annual inventory holding cost rate is 25% and it costs this coffee shop 20$ to place an order with the bean supplier. if the bean supplier offers a 7% discount on orders of 400 bags or more and 10% discount for 900 bags or more. A) What is the optimal order quantity for the coffee...
1) Television Haven buys televisions from a manufacturer and then sells them to department stores. Television...
1) Television Haven buys televisions from a manufacturer and then sells them to department stores. Television Haven is most likely a: a) Producer b) retailer c) Consumer d) Wholesaler e) marketer 2) -------------is one of the most difficult takes for managers. However, doing so is essential because it gives employees feedback and generates information about the quality of the firms selection, training, and development activities a) Performance appraisal b) Recruiting employees c) competition analysis d) Development appraisal e) Policy evaluation...
An investor buys a stock for $40 per share and simultaneously sells a call option on...
An investor buys a stock for $40 per share and simultaneously sells a call option on the stock with an exercise price of $42 for a premium of $3 per share. Ignoring the dividends and transaction costs, what is the maximum profit the writer of this covered call can earn if the position is held to expiration?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT