Problem tres Enoch Thompson bakery prepares all its cakes between 4a – 6am so th

ID: 390352 • Letter: P

Question

Problem tres

Enoch Thompson bakery prepares all its cakes between 4a – 6am so they will be fresh when customers arrive.

At the end of the day, leftover cakes are always sold, but at a 70% discount off the regular price of $12. The

cost of baking a cake is $5.

(a) Suppose demand is estimated to be normally distributed, with a mean of 20 and a standard deviation of 5.

How many cakes should the company bake each morning?

(5 marks)

(b) Suppose demand is estimated to be uniformly distributed between 16 – 30 cakes. How many cakes should

the company bake each morning?

(4 marks)

morning? What is Enoch’s expected daily profit?

(3 + 4 = 7 marks)

Demand 15 20 30 35 45 Probability .15 .25 .40 .15 .05

(a)

Underage cost, Cu = 12-5 = 7

Overage cost, Co = 5 - 12*(1-70%) = 1.4

Critical ratio = Cu/(Cu+Co) = 7/(7+1.4) = 0.833

z = NORNSINV(0.833) = 0.9674

Optimal number of cakes to bake = Mean demand + z*Std dev of demand

= 20 + 0.9674*5

= 25 cakes

(b) For uniformly demand, optimal number of cakes to bake = 16 + 0.9674*(30-16) = 27.7 ~ 28 cakes

look for cumulative probability, just greater than critical ratio of 0.8333, in the above table. Corresponding demand level is 35.

Optimal number of cakes to bake, Q = 35 cakes

Expected shortage, L = (45-35)*0.05 = 0.5

Average demand, d = 15*0.15+20*0.25+30*0.4+35*0.15+45*0.05 = 26.75

Expected sales, S = d - L = 26.75 - 0.5 = 26.25

Expected overage, V = Q - S = 35 - 26.25 = 8.75

Expected daily profit = S*Cu - V*Co = 26.25*7 - 8.75*1.4 = $ 171.5

Demand Probability Cumulative Probability 0 15 0.15 0.15 20 0.25 0.4 30 0.4 0.8 35 0.15 0.95 45 0.05 1

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.