Statistical Decision Making in Uncertainty - Research Paper Example

Every hamburger that is sold results in a profit of $ 1 for the restaurant. Every hamburger that remains unsold is wasted and results in a loss of $ 2 for the restaurant. This $ 2 is the cost of preparing a hamburger which includes the costs of the ingredients and other overheads.

The Decision involved: The restaurant wants to know how many hamburgers it should prepare every day so that its profit is maximized.

[Note: Conditional profit = Profit from selling one unit * number of units of hamburgers sold – Loss from one unsold hamburger * (number of units of hamburgers prepared – number of units of hamburgers sold).

Expected profit = Conditional profit * probability]

The optimal decision: Now the expected profits of the restaurant for each of the five scenarios have been calculated. The expected profits are:

If the restaurant prepares 200 burgers each day then its expected profit is: $ 110

If the restaurant prepares 400 burgers every day then its expected profit is:-$80

If the restaurant prepares 100 burgers every day then its expected profit is: $ 100

If the restaurant prepares 300 burgers every day then its expected profit is: $ 45

If the restaurant prepares 500 burgers every day then its expected profit is: -$ 235.

Therefore the optimal decision for the restaurant should be to prepare 200 hamburgers every day. This will maximize its profit to $ 110.

The trade-off between accuracy (perfect information) and its cost:

Now the restaurant chain is contemplating taking the help of a consultancy. The consultancy guarantees that it will give the restaurant the perfect forecast or perfect information about its daily sales. With the perfect information, the restaurant will know in advance how many hamburgers will be sold each day.