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

1   all nations face the problem of scarcity because there are limited resources and unlimited wants. nations do not have enough factors of production to produce everything that their population wants. entrepreneurial resources initiate businesses to make new goods and services; labor resources produce goods and services.

2 there are four factors of production: natural resources, labor resources, capital resources, and entrepreneurial resources. natural resources are raw materials from nature that are used to produce goods. trees, water, and grains are natural resources. some natural resources, such as wheat and cattle, are renewable

3 wants

things that you do not need to have in order to survive, but would like to have

needs

things that you must have in order to survive

goods

physical products

services

tasks that a business perform for customers

resources

items that people can use to make or obtain what they need or want

determine

to settle or decide by choice of alternatives or possiblities

4 i really dont know