The maximum revenue generated is $160000.
Given that, the revenue function for a sporting goods company is given by R(x) = x⋅p(x) dollars where x is the number of units sold and p(x) = 400−0.25x is the unit price. And we have to find the maximum revenue. Let's proceed to solve this question.
R(x) = x⋅p(x)
And, p(x) = 400−0.25x
Put the value of p(x) in R(x), we get
R(x) = x(400−0.25x)
R(x) = 400x - 0.25x²
This is the equation for a parabola. The maximum can be found at the vertex of the parabola using the formula:
x = -b/2a from the parabolic equation ax²+bx+c where a = -0.25, b = 400 for this case.
Now, calculating the value of x, we get
x = -(400)/2×-0.25
x = 400/0.5
x = 4000/5
x = 800
The value of x comes out to be 800. Now, we will be calculating the revenue at x = 800 and it will be the maximum one.
R(800) = 400x - 0.25x²
= 400×800 - 0.25(800)²
= 320000 - 160000
= 160000
Therefore, the maximum revenue generated is $160000.
Hence, $160000 is the required answer.
Learn more in depth about revenue function problems at brainly.com/question/25623677
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<u>b = 1/6 r w</u>
Multiply each side by 6 : 6b = r w
Divide each side by 'w' : <em>6b / w = r
</em>
The rate of change is $55 per hour. The means that the hourly rate of the designer is $55 per hour
<h3>Linear equation</h3>
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the line and m is the y intercept.
Let y represent the total cost of hiring for x hours. Hence:
- Using the points (0, 125) and (15, 950)
The rate of change is $55 per hour. The means that the hourly rate of the designer is $55 per hour
Find out more on linear equation at: brainly.com/question/14323743
Answer:1 4/5
Step-by-step explanation:
