Demand for devil's food whipped-cream layer cake at a local pastry shop can be approximated using a Poisson distribution with a mean of six per day. The manager estimates it costs $9 to prepare each cake. Fresh cakes sell for $12. Day-old cakes sell for $9 each. What stocking level is appropriate if one-half of the day-old cakes are sold and the rest thrown out?

The stocking level that is appropriate if one-half of the day-old cakes are sold and the rest thrown out is 5 cakes because, to maintain a service level greater or higher than 0.4 the shop should keep up the stocking level of 5 cakes

Explanation:

Solution

Given that:

The manager estimates it costs for (production cost) = $9

The selling cost for the cakes is = $12

The price for a day old cake sells for = $9

Now,

We must find the stocking level by applying the following steps:

The first step is to find the service level by using the formula below:

SL = Cs/Cs + Ce this is the equation (1)

Where,

Cs = The shortage of cost per unit = Rev - Cost

= $12-$9

=$3 per cake

Ce = The excess cost which is,

Ce = Cost - Salvage

= $9 - (1/2) * $9

=$4.50 for each cake

For the second step we replace the values equation 1 in other to find the service level as shown below:

SL = 3/3 + 4.50

=0.4

For the third step we have to apply the cumulative frequencies fro a mean 6.0 derived from the Poisson Table of probabilities. the values are shown below:

We now have the following:

Demand Cumulative Frequencies

0 0.003

1 0.017

2 0.062

3 0.0151

4 0.285

5 0.446

6 0.606

Thus,

After the comparison from the Table for us to maintain a service level greater or higher than 0.4 the shop should keep up the stocking level of 5 cakes