The demand for birthday cakes sold by a local bakery is estimated to follow an e

Question

The demand for birthday cakes sold by a local bakery is estimated to follow an exponential distribution with a mean of 20 cakes. Each birthday cake costs the owner of the bakery $7.50 to make and are sold for $12 per cake. If a customer arrives in the bakery to buy a birthday cake, and none is available, the owner gives the customer a discount voucher costing $5 as a goodwill gesture. Any birthday cakes left over at the end of the day can be sold for $6 per cake. i) How many birthday cakes should the bakery make for sale? (ii) If birthday cakes left over at the end of the day cannot be sold, but instead must be disposed of at a cost of $3 per cake, how many birthday cakes should instead be baked for sale? Use Inventory Models to solve the question.

Explanation / Answer

Answering the 1st question. The details are given below:

Cost price of 1 cake = $7.5

Selling price of 1 cake = $12

Salvage value of 1 cake = $6

Cost of underage, Cu = $ (12-7.5) = $ 4.5

Cost of overage, Co = $ (7.5-6) = $ 1.5

So the critical value, Cv = Cu/(Cu+Co) = 4.5/6 = 0.75

So, Probability (Demand<Q) = 0.75 where Q is the optimal quantity to be made

We know, Q = -LN(1-p)/Lambda, Here, Lambda = 1/20 = 0.05

So, using excel , Q = -LN(1-.75)/0.05 = 27.72

So answer to question 1 is 28.

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