Optimizing Revenue for a Sports Banquet

In summary, the hall charges $30 per person for a sports banquet and decreases the price by $10 per person for every group of over 50 people. Revenue is a multivariable function of the number of people in excess of 50, q, and the price per person, p. The function is R(q, p) = 1700 - 10q. To find the maximum revenue, we need to write a constraint equation for the price in terms of q and use the method of Lagrange Multipliers.
  • #1
bb155
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A hall charges $30 per person for a sports banquet. For every group of over 50, the hall will decrease the price by $10 per person, in excess of 50 people.

a. Write revenue as a multivariable function of the number of people, q, in excess of 50 and the price per person, p.

b.Write a constraint equation for the price in terms of the number of people in excess of 50

c.Maximize the revenue under the contstraint using the method of Lagrange Multipliers.

I just can't figure out b and c.. can anyone lend some help? As far as #A I have found that Revenue = 1700-10q and that when q=85 revenue is maximized.
 
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  • #2
bb155 said:
A hall charges $30 per person for a sports banquet. For every group of over 50, the hall will decrease the price by $10 per person, in excess of 50 people.

a. Write revenue as a multivariable function of the number of people, q, in excess of 50 and the price per person, p.

b.Write a constraint equation for the price in terms of the number of people in excess of 50

c.Maximize the revenue under the contstraint using the method of Lagrange Multipliers.

I just can't figure out b and c.. can anyone lend some help? As far as #A I have found that Revenue = 1700-10q and that when q=85 revenue is maximized.
Part a asks for the revenue as a function of q and p, R(q, p). What did you get as that function?
 

FAQ: Optimizing Revenue for a Sports Banquet

What is a multivariable function?

A multivariable function is a type of mathematical function that takes in more than one variable as input and produces a corresponding output. It is typically denoted as f(x, y) or z = f(x, y) and can be graphed in three-dimensional space.

How is a multivariable function different from a single variable function?

A single variable function only takes one input, typically denoted as x, and produces one output. A multivariable function, on the other hand, takes in multiple inputs and can produce multiple outputs. This allows for a more complex relationship between the variables.

What are the applications of multivariable functions?

Multivariable functions are commonly used in fields such as physics, economics, engineering, and statistics to model and analyze real-world systems that involve multiple variables. They are also used in optimization and machine learning algorithms.

How do you graph a multivariable function?

To graph a multivariable function, you can use a three-dimensional graphing tool or plot individual points to create a surface. It is also possible to create contour maps, which show the level curves of the function in two-dimensional space.

What are some common techniques for solving multivariable functions?

Some common techniques for solving multivariable functions include partial derivatives, gradient descent, and Lagrange multipliers. These methods allow for finding the maximum or minimum values of the function, as well as determining the rate of change of the function with respect to each variable.

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