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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?

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Answer:

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

The appropriate stocking level that is appropriate if one-half of the day-old cakes are sold and the rest thrown out is 5 cakes.

The following information are given:

  • Production cost for each cake = $9
  • Selling cost for the cakes = $12
  • The price for a day old cake sells = $9

Firstly, we need to calculate the service level which will be:

SL = Cs/Cs +Ce

where the shortage of cost per unit (Css) will be:

= $12 - $9

= $3 per cake

The excess cost (Ce) will be

= $9- [1/2 × $9]

= $9 - $4.50

=$4.50 for each cake

Therefore, the service level will be:

SL = Cs/Cs +Ce

SL = 3/(3 +4.50)

SL = 3/7.50

Services level = 0.4

Then, the cumulative frequencies will be depicted which will be:

 0                            0.003

 1                             0.017

 2                            0.062

 3                            0.0151

 4                            0.285

 5                           0.446

 6                            0.606  

Therefore, looking at the table, appropriate stocking level that is appropriate if one-half of the day-old cakes are sold and the rest thrown out is 5 cakes.

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