The UTD cafeteria offers scones for $1.50 each from 8am to 3pm. The scones are o
ID: 3217282 • Letter: T
Question
The UTD cafeteria offers scones for $1.50 each from 8am to 3pm. The scones are ordered from their supplier at the start of each day and delivered before the store opens. The supplier charges $0.75 per scone. Assume that all leftover scones, if any, are thrown away when they close. Demand for scones before 3pm at the cafeteria is variable but can only take values between 40 and 50, with probabilities given in the following table. Fill in the cumulative probability column and proceed with the questions below.
Number of customers: 40 41 42 43 44 45 46 47 48 49 50
Probability: 0.05 0.05 0.15 0.20 0.15 0.10 0.10 0.10 0.05 0.025 0.025
Cumulativ Probability: 0.05 0.10 0.25 0.45 0.60 0.70 0.80 0.90 0.95 0.975 1.00
a) What is the expected number of customers who want to buy a scone on a given day? Answer: 44.23 customers
b) Yesterday, the cafeteria ordered 45 scones and 43 customers bought a scone between 8am and 3pm. What was their profit then? (include their profit on chips sold instead of scones). Answer: P = $30.75
c) Two days ago, the cafeteria ordered 45 scones and 49 customers came wanting to buy a scone between 8am and 3pm. What was their profit then? Answer: P = $33.75
d) How many scones should the cafeteria order to maximize expected profit?
e) How many scones should the cafeteria order to guarantee that they have enough schones to satisfy all the customers who come before 3pm, at least 85% of the time?
**************** PLEASE ANSWER QUESTIONS d and e. Thank you! ******************************************************
a 975 naarantee that they hewe moush scteel toExplanation / Answer
Probability of selling unit
1
0.95
0.9
44 scones should the cafeteria order to maximize expected profit
e) 46 scones should the cafeteria order to guarantee that they have enough schones to satisfy all the customers who come before 3pm, at least 85% of the time
No. of customers Probability Cumulative probabilityProbability of selling unit
Probability of not selling Expected Profit Expected loss Expected net profit 40 0.05 0.051
0 0.75 0 0.75 41 0.05 0.10.95
0.05 0.7125 0.0375 0.675 42 0.15 0.250.9
0.1 0.675 0.075 0.6 43 0.2 0.45 0.75 0.25 0.5625 0.1875 0.375 44 0.15 0.6 0.55 0.45 0.4125 0.3375 0.075 45 0.1 0.7 0.4 0.6 0.3 0.45 -0.15 46 0.1 0.8 0.3 0.7 0.225 0.525 -0.3 47 0.1 0.9 0.2 0.8 0.15 0.6 -0.45 48 0.05 0.95 0.1 0.9 0.075 0.675 -0.6 49 0.025 0.975 0.05 0.95 0.0375 0.7125 -0.675 50 0.025 1 0.025 0.975 0.01875 0.73125 -0.7125Related Questions
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