Fashion Shoes Inc. is a retailer that purchases sports shoes from various suppli
ID: 358731 • Letter: F
Question
Fashion Shoes Inc. is a retailer that purchases sports shoes from various suppliers and sells to the end customers. Among various vendors, Fashion Shoes Inc. works closely with an imminent shoe manufacturing company, Zodiac. There are several models Fashion Shoes purchases from Zodiac and sells in its own stores; however, in particular, a model of sports shoes called “Aerospace” sells very well. The manufacturing cost for producing this model of shoes is $25 dollars per pair. The transportation and handling cost that accrues for Fashion Shoes per pair of Aerospace shoes is $15.
1. (15 points) Suppose that the demand equation is roughly estimated to be D = 10,000-100p for the Aerospace Model. If the Zodiac and Fashion Shoes each try to maximize their own profits, what would be the price charged by Zodiac for Aerospace shoes, and what would be the selling price of the end item? How much profit would each company obtain?
2. (15 points) Now suppose that the two companies can come to an agreement by using a “revenue sharing contract”. According to the terms of the contract, the two parties set the sales price together, and share the net profit according to a 60%-40% rule (40% of the profit is earned by Fashion Shoes, and 60% will belong to Zodiac). Find net profits of the two firms in this setting. What is the improvement in profits compared with the initial situation?
3. (30 points) Fashion Shoes Inc. wants to do inventory planning to minimize the costs. Each time they make a purchase from Zodiac, the total costs for processing the purchase order and the transportation costs turn out to be $400. Moreover, for each model ordered and delivered on the same truck, an additional fixed cost of $100 is incurred for receiving, handling and storage. These costs are fixed regardless of the quantity or the type of model purchased. The inventory holding cost is 20% of the purchase price of the sports shoes. If Fashion Shoes buys the Aerospace shoes at a price of $45 per pair from Zodiac, and if the total annual demand is the sum of the demands in the above table, what should be the economic order quantity (EOQ) for ordering Aerospace shoes only? What if they order Aerospace together with another Zodiac model, Infinity, which has a total yearly demand of 5000 units and a purchase cost of $30: what will be the ordering quantities and total annual costs then? What is the amount of savings obtained by ordering together over ordering separately?
Explanation / Answer
1. D = 10,000- 100p
Add 100p to both sides: D+100p= 10,000
therefore, p= (10,000-D) /100
p=100 - 0.01D
To determine the total revenue, multiply both sides by D
TR = pD = 100D - 0.01D2
Total Profit, P Zodiac = 100D- 0.01D2 - 25
PFashion shoes = 100D - 0.01 D2 -25-15
dP/dD = 0 for max profit
100-0.02D=0 -----------therefore, D = 100/0.02 = 10000/2 = 5000
For Zodiac : 5000= 10000-100p therefore, p = $50
Maximum profit , PZodiac = 50 ( 10000-100*50) - 25*5000 = $1,25,000
PFashion shoes Inc. = 50 (10,000-100*50) - (25 + 15) *5000 = $50,000
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