Question

2. There is no demand for an item when the price is $800. However, there is a demand for
100 items when the price is $600. The supplier will not provide any of the items if the unit price is
$300 or below. The supplier will provide 150 items when the unit price is $375.

a. Write the demand equation. Hint, let x be items and y be $.

b. Write the supply equation. Hint, let x be items and y be $.

c. Sketch the graph of supply and demand functions, and find the equilibrium point.

Answer 1

Using linear functions, it is found that:

a) The demand function is: $y = -2x + 800, x \leq 400$

b) The supply function is: $y = 0.5x + 300, x \geq 0$

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:

$y = mx + b$

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:

$m = \frac{600 - 800}{100 - 0} = -2$

• Also, when x = 0, y = 800, thus $b = 800$

Then:

$y = -2x + 800, x \leq 400$

As the price has to be positive.

Item b:

• Points (0, 300) and (150, 375).
• The slope is:

$m = \frac{375 - 300}{150 - 0} = 0.5$

• The y-intercept is $b = 300$

Thus:

$y = 0.5x + 300, x \geq 0$

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