Reference no: EM133349248

Problem 1
Emma Queen decided to open a food stand at the Bothell Friday Market at Beardslee Village. She planned to buy strawberries from her local farm and sell them at the Bothel Market on Fridays. She estimated cost of renting a truck to transport strawberries is $20.00 per week. The cost of strawberries to Emma is $0.90 per pound. Emma sold the strawberries on Friday between 10 am and 6 pm at the booth at the Farmer's Market. The booth rental is $40.00 per week. The strawberries are sold to the customers for $1.20 per pound. Strawberries not sold by 6 pm were discarded. Demand for strawberries was unpredictable, Queen estimated weekly demand before placing an order with the farmer and renting the truck to transport them. Based on demand from similar entrepreneurial ventures and interviews with potential customers, she estimated that weekly demand for the strawberries was normally distributed with a mean of 350 lbs and a standard deviation of 100 lbs.

a. How many lbs of strawberries should Queen stock? What is the profit at this stocking quantity?

b. Verify that the value derived in part (a) is consistent with the optimal stocking quantity in the Newsvendor model.

Problem 2
Queen came to believe after six months of operations that the demand for strawberries could be increased by wiping the strawberries and arranging them neatly in small wicker baskets. The demand was a function of the amount of time she invested in arranging the strawberries. Queen kept records of time she spent each week arranging the berries. Using this data, she derived the demand function: D= 350+α √h= 350 + 80 √h where D is the weekly demand for the strawberries and h is the number of hours Queen spent arranging the strawberries in baskets.

As before, Queen forecast following week's demand every week based on the hours spend arranging the strawberries and used this demand forecast to determine her stocking quantity.

a. How many hours should Queen spend weekly in arranging the strawberries? Assume opportunity cost of her time to be $5.00 per hr. (Optimal stocking quantity Q is computed by the spreadsheet based on the newsvendor formula for your choice of h)

b. What explains Queen's choice of effort level h?

c. Compare the optimal profit under this scenario with the optimal profit derived in
Problem #1. If they are different, why is one of them higher than the other?

Problem 3
Queen gets very busy over the next few months and decides to hand over the retailing portion of the business to Rony Halibut. Halibut would be running the stand at the farmer's market and pay the weekly rent of $40.00 to the landlord every week. He was to estimate the demand for strawberries based on the observed demand previous week. Strawberries purchased from Queen at $1.05 per pound were to be delivered to the farmer's market stand any strawberries left over at the end of the week.

a. Assuming h= 2 (i.e., Queen has spent 2 hours arranging strawberries), what would Halibut's stocking quantity be?

b. Why does the optimal stocking quantity differ from the optimal stocking quantity identified in Problem #2? Is the result here consistent with the newsvendor formula? Why or why not?

c. Now try newsboy calculation for differentiated channel, (i.e. to maximize Rony's profit) to see what happens to Queen's profit. How does her optimal effort in this question differ from the answer to question 2? Why?

d. How would changing the transfer price from the current value of $1.05 per lbs impact Queen's effort level and Halibut's stocking decision?

e. What conclusions can you draw about stocking and effort levels in a differentiated channel
versus an integrated firm that manufactures and retails its product?

Problem 4
After a year of operations, expected weekly demand remained at 350 and the standard deviation of weekly demand at 100 As in Problem #3, Halibut retailed strawberries at $1.20 per lbs, which were purchased from Queen at $1.05 per lbs. Halibut was responsible for unsold strawberries. Having virtually no competition from other farmer's market stands and being firmly established at the farmer's market, Halibut broadened the product line to include newspapers and magazines. He became friendly with the customers and regulars.

Inspired by the success of strawberry sales, Halibut decided to include blueberries to his portfolio at the farmer's market stand. Halibut lived very close to the farmer's market and was growing blueberries in his large yard. So, he didn't need to stock and inventory of blueberries, and, if a customer demanded blueberries, he could go & pick them from his yard and bring them in no time. Marginal cost to pick and transport the blueberries was $0.70 per pound, and the blueberries retailed for $0.95 per lbs.

Queen believed blueberries posed no threat to her strawberries, since they were grown on a yard with no special attention to them during the time they grew. Halibut agreed that customers wouldn't choose blueberries over strawberries, but he realized that he frequently stocked out of strawberries. He estimated that approximately 30.00% of the customers who experienced a stockout from strawberries would buy blueberries. The other 70.00% would not buy berries at the stand that week.

a. If you were Halibut, how many pounds of strawberries would you stock? Compare your stocking decision with the optimal
decision from Problem #3a

b. Why does optimal stocking quantity differ from the answers given in Problems #1, #2 and #3? How is this answer consistent with the logic of the newsvendor model.

c. Halibut 's stand was constrained for space as he continued to add new products. To get a better idea of the true profitability for each product, he decided to allocate the cost of real estate according to space occupied by each product. If he figured weekly real estate costs for each additional lbs at approximately $0.02 how would this impact his stocking decision? Why?

Problem 5
Responding to competition from the blueberries, Queen invested in an advertising campaign, aimed at making customers more loyal to the strawberries. As a result of the ad campaign, few customers were willing to switch to the blueberries when Halibut stocked out of the strawberries, choosing instead to not purchase either the strawberries or the blueberries. Owing to higher customer loyalty to the strawberries, demand for the blueberries was low, and Halibut eventually decided to stop selling blueberries. Thus, the situation in Farmer's Market Stand 'reverted to the scenario described in problem # 3 above (i.e., Queen sold the strawberries to Halibut at a wholesale price of $1.05 per lbs, who did not carry competing blueberries).

Queen, however, noted that Halibut's fill rate was low even though he was no longer carrying the blueberries; she noted (from spreadsheet #3c) that he stocked approximately 331 lbs, even though expected weekly demand for the strawberries was around 446 lbs. Fill rate on the strawberries was close to 91.00%

When Queen spoke to Halibut about stocking more strawberries, he pointed out that he was stocking what was optimal for his stand. "I even used the newsvendor formula,"he pointed out defensively, adding: "I will offer you a solution. Why don't you buy back unsold strawberries at a salvage price close to the price at which you sell me the strawberries. You could even sell me all the strawberries on consignment (i.e., buy back unsold lbs at the wholesale price). I will surely buy more if you buy back unsold strawberries."

a. Assume Queen chages a wholesale price of $1.05 per lbs of strawberries. How does her buyback price impact Halbut's stocking quantity? What buyback price would maximize channel profit? How much does Halibut stock under this buy-back plan?

b. Identify the combination of transfer price and buy-back price that maximizes expected weekly profit for the channel. How does this number compare with the expected weekly profit from problem #2 (vertically integrated channel) and problem #3 (no buy-back)

c. How would Halibut's stocking decision, and Queen's effort decision be altered if Queen insisted on a daily franchise fee in addition to the margins' she earned ( a franchise fee would require Halibut to pay Queen a fixed fee every week to be able to carry the strawberries in his stand)