Mason MBA operates a beach stall every summer. Mason needs to determine how many
ID: 463956 • Letter: M
Question
Mason MBA operates a beach stall every summer. Mason needs to determine how many umbrellas to stock for this season. He uses the same supplier each year who charges $18 per umbrella. Mason knows the supplier’s cost is $3.50. Based on experience and his weather app, Mason has determined that demand will follow the discrete distribution shown below when he charges a price of $25 per umbrella. If he can’t sell the umbrellas, he expects to toss them out at no cost. Provide your answer under each question. Please show your calculations in this document or attach a spreadsheet. Demand 125 150 175 200 225 Probability 0.1 0.1 0.2 0.3 0.3 a. (4 points) How many umbrellas should Mason buy from the supplier to maximize his profits? b. (4 points) What is his expected profit? c. (2 points) What is the supplier’s profit? d. (1 points) What is the total supply chain profit?
Explanation / Answer
Demand 125 150 175 200 225
Probability 0.1 0.1 0.2 0.3 0.3
Expected demand = demand t * probability t
= 125 * 0.1 + 150 *0.1 + 175 * 0.2 + 200 * 0.3 + 225 * 0.3 = 190
a. How many umbrellas should Mason buy from the supplier to maximize his profits?
Optimal order quantity Q = D+ z
Where D is the average demand = 190 umbrellas
And is the standard deviation of demand is not given therefore assuming it as 0
Optimal order quantity Q = D = 190 umbrellas
b. What is his expected profit?
The expected profit = (profit from one umbrella) * Optimal order quantity
= ($ 25- $ 18) * 190 = $ 7 * 190 = $1330
c. What is the supplier’s profit?
Supplier’s profit == (sale price of one umbrella for supplier – cost of one umbrella) * Optimal order quantity
= ( $ 18 - $ 3.5) * 190 = $ 2755
d. What is the total supply chain profit?
Total supply chain profit = supplier’s profit + Mason’s profit = $ 2755 + $1330 = $ 4085