NO LINKS NOT MULTIPLE CHOICE!! a. Sketch a graph to model Seattle's cost structure over the domain [0, 42,000]. Be sure to label the axes and any endpoints where the graph breaks.

b. Describe the function over each part of its domain. State whether it is constant, increasing or decreasing, and state the slope over each part. ​

Step-by-step explanation:

In the graphs below.    I'm feel like the person that asked this question didn't understand that the lines would be reallly tuff to see.. as they are less than one.. but the graph is going out to 42,000  :0

as you can see in the graphs, i've used the given formulas  :P

Part (a)

The graph is shown below. It's a piecewise function composed of 3 parts: Two flat horizontal segments and a decreasing segment.

Note the use of open holes at points C and E. They tell the reader that the specific point is not part of the function. For example, point C at (8000,0.75) is an open hole since the second piece has x = 8000 excluded. In other words, the domain for the second piece is which says to exclude 8000 but to include 20,000.

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Part (b)

The flat parts are due to the two first pieces being constant functions. Regardless of what x is on those portions, the cost per unit stays the same. We see that the cost starts off at 35 cents per unit (green segment), then it jumps to 75 cents per unit (blue segment).

So far the costs have been constant, but once we get to the red curve portion, then the costs decrease as x increases. Note that 1/(200,000) = 0.000005 which means the costs are decreasing by 0.000005 dollars per unit. Let's multiply that by 10,000 to get 10,000*0.000005 = 0.05

So for the red portion, the costs are decreasing by $0.05 per 10,000 units, or they are decreasing by 5 cents per 10,000 units. When x > 20000, the lowest we can get the cost is at 62 cents per unit. This is when production is at max capacity (42,000 units).

If you wanted the cost per unit to be as small as possible, and x didn't have to be larger than 20 thousand, then you'd stick to the green line. However, the drawback here is that you can only produce at max 8000 units.

simplify the expression

you get,