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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Answer:
The cost of the diamond last year is x = $ 830
Step-by-step explanation:
Let the cost of diamond last year = x
the cost of diamond present year = y
Given that diamond today cost ten dollars more than twice what it cost last year.
⇒ y = 2 x + 10 ------ (1)
The sum of the cost (last year and this year) is = $ 2500
⇒ x + y = $ 2500 -------- (2)
Put the value of y in equation (2) from equation (1), we get
⇒ 2 x + 10 + x = $ 2500
⇒ 3 x = 2490
⇒ x = $ 830
& y = 2500 - 830
⇒ y = $ 1670
Therefore the cost of the diamond last year is x = $ 830
2x+y=-10
Multiply both side by 3
2x*3+y*3=-10*3
6x+3y=-30
3x-y=0
Multiply both side by 2
3x*2-y*2=0*2
6x-2y=0
Next, use substitute property
6x+3y=-30
-
6x-2y=0
=
y=-30
3x-y=0
Substitute y with -30
3x-30=0
Add 30 to each side
3x-30+30=0+30
3x=30
Divided both side by 3
3x/3=30/3
x=10, so the solution pair is (10,-30). In this case, there is the first way to solve these two equation.
Then, I would use equation 3x+1.5y=-15 in this question by multiply 2x+y=-10 by multiplying both side by 3/2 to eliminate x and to solve variables for y. Hope it help!
Answer:
Personally I'll pick algebra with finance, maybe you'll want to start a business in the future. Then this will surely come in handy.
Step-by-step explanation:
