Optimization Problems
Word Problems
An Easy 1st Example
Solution
2nd Example
Solution to Fence Problem
3rd Example
Solution to Ticket Problem
4th Example
Solution to Closest Pt Problem
The Rest of the Solution
5th Example (a harder problem)
Continuation of 5th Example
Continuation of 5th Example
Completion of 5th Example
6th Example
Solution to the Box Problem
which means
Applications to Business
Some Notation
Let x be the number of items
sold or produced
• C(x) = total cost of
producing or selling x items
• R(x) = total revenue when x
items are sold
• P(x) = total profit when x
items are sold
• p(x) = price that will result
in x items being sold
Some formulas:
• P(x) = R(x) – C(x)
• R(x) = x p(x)
The Marginal Cost
A Simple Example of Marginal Cost
Note: the 1,000 represents the set up costs or fixed costs.
Example
Note: The equation for p(x) is called a price-demand equation.
Continuation of Example
More Questions
And More Questions
Solutions to the 8 Questions
One Last Example
Solution to Can Problem