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Chapter 17: Problem 32

A restaurateur anticipates serving about 180 people on a Friday evening, and believes that about \(20 \%\) of the patrons will order the chef's steak special. How many of those meals should he plan on serving in order to be pretty sure of having enough steaks on hand to meet customer demand? Justify your answer, including an explanation of what "pretty sure" means to you.

Short Answer

Expert verified
Prepare 40 steak specials.

Step by step solution

01

Understand the Problem

Identify that we need to find the number of steak specials anticipated to be ordered given that 20% of patrons are expected to order it, and there are 180 patrons in total.
02

Calculate the Expected Number of Orders

Multiply the total number of patrons by the percentage that will order the steak special. Use the formula: \[ \text{Expected Orders} = \text{Total Patrons} \times \text{Percentage ordering Steak Special} \] Substitute \(180\) for the total patrons and \(0.2\) for the percentage:\[ \text{Expected Orders} = 180 \times 0.2 = 36 \] This means we expect 36 orders for the steak special.
03

Add a Buffer to Be "Pretty Sure"

Being "pretty sure" means accounting for a slight increase in the number of orders to ensure you don't run out of steak specials. It is reasonable to add a small buffer, such as 10%, to the expected orders. Calculate the buffer: \[ \text{Buffer Amount} = \text{Expected Orders} \times 0.10 = 36 \times 0.10 = 3.6 \] Round up since you can't prepare a fraction of a meal, so the buffer is 4 extra steak specials.
04

Determine the Total Number of Steaks to Prepare

Add the buffer to the expected number of orders to determine the total number of steaks to prepare:\[ \text{Total Steaks} = \text{Expected Orders} + \text{Buffer Amount} = 36 + 4 = 40 \] Therefore, the restaurateur should plan on approximately 40 steak specials.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Expected Value
Expected value is a crucial concept in probability and statistics. It represents the average or mean outcome you would expect to see based on a specific scenario or repeated trials. It's like having a prediction based on probabilities. For those trying to optimize decisions based on predictions, expected value serves as a reliable guide.

In the context of a restaurant, expected value helps in planning the number of meals to prepare. Imagine you have a restaurant owner who knows from past data that 20% of patrons order the steak special. Knowing that 180 people are expected, he can predict the outcome using the expected value formula:
  • Expected Orders = Total Patrons 脳 Percentage ordering Steak Special
In our problem, the calculation would be:
  • Expected Orders = 180 脳 0.2 = 36.
This tells the owner that, on average, 36 out of 180 patrons will order the special. By understanding expected value, businesses can better prepare resources and manage expectations.
Buffer Stock Calculation
Buffer stock calculations are all about handling uncertainty and risk. In our scenario, the restaurant owner wants to make sure there's enough steak to meet customer demand, even if more people than expected decide on the steak special.

"Being pretty sure" means planning ahead by having a little extra stock, also known as a buffer or safety stock, to handle unexpected demand spikes. To calculate this buffer, a small fraction of the expected order is usually added:
  • Buffer Amount = Expected Orders 脳 Extra Percentage
In our case, if the extra percentage is 10%, the calculation would be:
  • Buffer Amount = 36 脳 0.10 = 3.6
Since preparing a fraction of a meal isn't possible, we round up to 4. This means preparing 4 additional steaks. Buffer stocks minimize the risk of running short, leaving customers satisfied and business operations smooth.
Percentage Calculation
Percentage calculations are fundamental in interpreting data in percentage terms. They help us understand parts of a whole, often bringing clarity to complex data sets. Every day, percentages play a crucial role in finance, surveys, and, as we see now, restaurant meal planning.

For the restaurant, determining how many meals to prepare involves simply applying a percentage to a total number. The percentage of meals ordered is 20% of the total expected patrons.
  • Percentage Calculation = Total Patrons 脳 Percentage
For the steak special, that meant taking 20% of 180 patrons:
  • Percentage Calculation = 180 脳 0.2 = 36
This shows that 36 expected customers will choose the special. By mastering simple percentage calculations, managers can quickly make sense of demand forecasts, aiding effective stock and resource management."

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Most popular questions from this chapter

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