The supply equation for the Wilkinson washable computer keyboard is p=0.03x+80. Where x is the quantity supplied per month and p is the unit price in dollars.
a) find the points that would be used to sketch a graph of the supply curve
b) what is the lowest price (theoretically) at which the supplier will make a washable keyboard available in the market?
I am stumped for both a and b.
For a, how would I know which numbers to plug in for a? For example, I tried plugging in p=0.03(0)+80=80 for (0,80) but I don't know what numbers I can plug in for the remaining points. Can they be any number?
Ah, the art of graphing supply curves! Let's break it down step by step.
a) To sketch a graph of the supply curve, we need to find a few points. The equation given to you is p = 0.03x + 80, where x is the quantity supplied per month and p is the unit price in dollars. To find points, we can choose different values for x and calculate the corresponding prices (p).
Since there's no specific information about the range of x values, we're free to choose any numbers that make sense. Let's pick a few values of x and find their corresponding p values for plotting:
Let's start with x = 0:
p = 0.03(0) + 80
p = 0 + 80
p = 80
So the first point is (0, 80).
Now let's try x = 100:
p = 0.03(100) + 80
p = 3 + 80
p = 83
The second point is (100, 83).
Feel free to choose a few more x values and calculate their corresponding p values. Once you have a few points, you can plot them and draw a line through them to sketch the supply curve.
b) The lowest price (theoretically) at which the supplier will make a washable keyboard available in the market can be found by plugging in the maximum value of x. However, since there's no specified range for x, we can assume it could be any positive value.
So, for the lowest possible price:
Let's plug in a very large value for x, say x = 1,000,000:
p = 0.03(1,000,000) + 80
p = 30,000 + 80
p = 30,080
Therefore, the lowest price the supplier will theoretically offer the washable keyboard is $30,080.
Keep in mind that this is a theoretical value and might not be practically feasible, but now you have a better understanding of the graph and the lowest price possible according to the equation.
To sketch a graph of the supply curve, you need to find multiple points that satisfy the supply equation. The equations represent a linear relationship between the quantity supplied (x) and the unit price (p).
a) To find the points for sketching the graph, you can choose any values for x and calculate the corresponding values for p using the supply equation. However, it's generally helpful to choose multiple values of x to get a better understanding of the relationship.
Let's choose some values for x and calculate the corresponding values for p:
1. x = 0: p = 0.03(0) + 80 = 80. This gives the point (0, 80).
2. x = 100: p = 0.03(100) + 80 = 83. This gives the point (100, 83).
3. x = 200: p = 0.03(200) + 80 = 86. This gives the point (200, 86).
You can choose more values for x if you like, but these three points are sufficient to sketch a basic graph of the supply curve.
b) The lowest price at which the supplier will make a washable keyboard available in the market can be determined by solving for p when x is at its minimum.
Since x represents the quantity supplied, it cannot be negative or zero. In this case, the lowest value that x can take is 1. To find the lowest price theoretically, plug x = 1 into the supply equation:
p = 0.03(1) + 80 = 80.03.
Therefore, the lowest price theoretically at which the supplier will make a washable keyboard available in the market is $80.03.
To determine the points that would be used to sketch a graph of the supply curve, you can choose various values for x and then calculate the corresponding values for p using the given equation p = 0.03x + 80. Here's how you can do it:
1. Select some values for x:
- You can start by choosing x = 0 to represent the quantity supplied when there is no production, which will give you the y-intercept of the supply curve.
- You can then choose a few more values for x such as 10, 20, and 30 (or any other values you prefer) to represent different levels of quantity supplied.
2. Calculate the corresponding values for p:
- For each chosen value of x, substitute it into the equation p = 0.03x + 80 and calculate the corresponding value for p.
For example:
- When x = 0, p = 0.03(0) + 80 = 80. Therefore, one point is (0, 80).
- When x = 10, p = 0.03(10) + 80 = 0.3 + 80 = 80.3. Another point is (10, 80.3).
- Repeat this process for the other chosen values of x.
Once you have the calculated values for p, you can plot them on a graph with x on the x-axis and p on the y-axis. Connect the plotted points with a smooth line to represent the supply curve.
For part b, to find the lowest price (theoretically) at which the supplier will make a washable keyboard available in the market, you need to determine the minimum value of p from the supply equation p = 0.03x + 80. Since the coefficient of x is positive, the value of p will increase as x increases. Therefore, the lowest price will occur when x is the smallest possible non-negative value. In this case, the smallest non-negative value for x is 0.
Substituting x = 0 into the equation, you get p = 0.03(0) + 80 = 0 + 80 = 80. Hence, theoretically, the lowest price at which the supplier will make a washable keyboard available in the market is $80.