The graph shows the number of servings in different amounts of frozen yogurt listed on a carton. Enter an equation that gives th
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We will investigate how to determine Hamilton paths and circuits
Hamilton path: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex can be different.
Hamilton circuit: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex must be the same!
As the starting point we can choose any of the points. We will choose point ( F ) and trace a path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex to be ( F ). Such a path is called a Hamilton circuit per definition.
We will choose a different point now. Lets choose ( E ) as our starting point and trace the path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex are different with be ( E ) and ( C ), respectively. Such a path is called a Hamilton path per definition.
One more thing to note is that all Hamilton circuits can be converted into a Hamilton path like follows:
The above path is a hamilton path that can be formed from the Hamilton circuit example.
But its not necessary for all Hamilton paths to form a Hamilton circuit! Unfortunately, this is not the case in the network given. Every point is in a closed loop i.e there is no loose end/vertex that is not connected by any other vertex.
The number of units of x that must be sold to break even is 12 units.
Explanation:
It is given that the cost function C(x) is given by
Also, the revenue function R(x) is given by
The break even point can be determined by equating the cost function and the revenue function.
Thus, we have,
Subtracting both sides by , we get,
Dividing both sides by , we have,
Thus, it takes 12 units to be sold to break even.
Hence, the number of units of x that must be sold to break even is 12 units.