Using linear functions, it is found that:
a) The demand function is: [tex]y = -2x + 800, x \leq 400[/tex]
b) The supply function is: [tex]y = 0.5x + 300, x \geq 0[/tex]
c) The graph is given at the end of this answer, and the equilibrium point is 200 items, at which the unit price is $400.
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A linear function has the following format:
[tex]y = mx + b[/tex]
In which
- m is the slope, which is the rate of change.
- b is the y-intercept, which is the value of x when y = 0.
Item a:
- For demand, there are two points: (0,800) and (100,600).
- The slope is change in y divided by change in x, thus:
[tex]m = \frac{600 - 800}{100 - 0} = -2[/tex]
- Also, when x = 0, y = 800, thus [tex]b = 800[/tex]
Then:
[tex]y = -2x + 800, x \leq 400[/tex]
As the price has to be positive.
Item b:
- Points (0, 300) and (150, 375).
- The slope is:
[tex]m = \frac{375 - 300}{150 - 0} = 0.5[/tex]
- The y-intercept is [tex]b = 300[/tex]
Thus:
[tex]y = 0.5x + 300, x \geq 0[/tex]
Item c:
- The functions are sketched on the graph given, considering demand in blue and supply in orange.
- The equilibrium point is where they are equal, thus at 200 items, at which the unit price is $200.
A similar problem is given at https://brainly.com/question/24615316
