Answer:
The profit function can be expressed as:
Profit = Revenue - Cost
Revenue = Price x Quantity
Price = p = 450,000 - 100x
Quantity = x
Cost = C = 500/x + 200x + x²
Substituting these values, we get:
Profit = (450,000 - 100x) x - (500/x + 200x + x²)
Simplifying this expression, we get:
Profit = -x² + 450,000x - 500 - 200x² - x³
To find the quantity that gives maximum profit, we need to differentiate the profit function with respect to x and set it equal to zero:
d(Profit)/dx = -3x² + 450,000 - 400x - 500/x²
Setting this derivative equal to zero and solving for x, we get:
3x³ - 450,000x² + 400x³ + 500 = 0
This equation can be solved numerically to obtain:
x ≈ 98.9
To confirm that this is a maximum, we can check the second derivative of the profit function:
d²(Profit)/dx² = -6x + 800/x³
At x = 98.9, this evaluates to:
d²(Profit)/dx² ≈ -2.71
Since the second derivative is negative, the profit function has a maximum at x ≈ 98.9.
The maximum profit can be found by substituting this value of x into the profit function:
Profit ≈ $20,007,710
To find the selling price that maximizes profit, we can use the demand function:
p = 450,000 - 100x
At x = 98.9, this evaluates to:
p ≈ $35,110
Therefore, the corporation should sell its product for $35,110 to maximize profit.
The area of the parallelogram is 60 square millimeters.
What is the parallelogram's base, b?
The base of the parallelogram is 60.
How to find?
To find the base of a parallelogram, we need to know its area and height. The area of a parallelogram is given by the formula:
A = b × h
where A is the area, b is the base, and h is the height.
In this case, we are given that the area of the parallelogram is 60 square millimeters. We do not know the height of the parallelogram, so we cannot solve for the base directly.
However, we do know that the area of a parallelogram is equal to the product of its base and height. So, if we can find the height of the parallelogram, we can then use the formula to solve for the base.
To find the height, we can use the formula:
h = A / b
where A is the area and b is the base.
Substituting the given values, we get:
h = 60 / b
Now, we still do not know the value of the base, but we can use this expression for the height to set up an equation that relates the base and height of the parallelogram.
We know that the opposite sides of a parallelogram are parallel and have the same length, so the height of the parallelogram is perpendicular to the base. Therefore, we can draw a perpendicular line from the height to the base, dividing the parallelogram into two congruent triangles.
Each triangle has an area of A/2, and its base and height are b and h, respectively. Therefore, we can set up the following equation:
A/2 = bh/2
Substituting the expression for the height, we get:
A/2 = b(60/b)/2
Simplifying, we get:
A/2 = 30
Multiplying both sides by 2, we get:
A = 60 = bh
Now we have an equation that relates the base and area of the parallelogram. Substituting the given value for the area, we get:
60 = b × h
Substituting the expression for the height, we get:
60 = b × (60 / b)
Simplifying, we get:
60 = 60
This equation is always true, which means that any value of b that satisfies the condition for a parallelogram (i.e., opposite sides are parallel and have the same length) will work. Therefore, we cannot determine the value of the base without additional information.
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By applying SAS congruence rule, you want to establish that triangle PQR =~ triangle KLM. It is given that PQ = KL and RP = MK. What additional information is needed to establish the congruence?
Answer:
Step-by-step explanation:
To establish the congruence of two triangles using the SAS (Side-Angle-Side) congruence rule, we need to know that two corresponding sides and the included angle are congruent.
In the given information, PQ = KL and RP = MK, but we do not know the measure of any included angle between the corresponding sides. Therefore, we need to know at least one angle that is congruent in both triangles to apply the SAS congruence rule.
Without additional information about an included angle, we cannot establish the congruence of triangle PQR and triangle KLM using the SAS congruence rule.
Find the median of these numbers: 2.9, 9.1, 5.2, 2.9, 8.7, 7.4
Answer: 6.3
Step-by-step explanation:
Answer:
4.45
Step-by-step explanation:
5.2 + 7.4 ÷ 2 = 8.9 ÷ 2 = 4.45
Correct me if im wrong! Thank you!UwU
g(x)=4x-(3x+7x/3) Find the slope and y=intercept. Express the intercept as an ordered pair. Simplify your answer.
Answer:
Slope: -(4/3)
Y-intercept: 0
Compute the voltage drop if the source voltage is 240V and the load voltage is 237V.
The voltage drop is the difference between the source voltage and the load voltage, which is 3V.
What is voltage drop?Voltage drop is the decrease of electric potential along the path of a current flowing in a circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated.
Voltage drop of the circuit conductors can be determined by multiplying the current of the circuit by the total resistance of the circuit conductors: VD = I x R.
The voltage drop can be calculated by subtracting the load voltage from the source voltage. In this case, the voltage drop is:
240V - 237V = 3V
Thus, the voltage drop is 3V.
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Help me on this one please.
Number 6 only.
Answer:
x=1.5
Step-by-step explanation:
Among all rectangles that have a perimeter of 172
, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.
Answer: 43x43 units 1849 units^2
Determine the product. Write your answer in scientific notation. (15.4 × 102) · (2.8 × 10–4) = ?
Answer:
Step-by-step explanation:
(15.4*102)*(2.8*10-4)
(1,570.8)*(28-4)
(1,570.8)*(24)
37,699.2
Evaluate the given expression and show the steps, please.
To find:-
[tex]\displaystyle \sum_{n=1}^{4} 2(3^{n - 1})[/tex]Answer:-
We need to evaluate,
[tex]\implies s_4=\displaystyle \sum_{n=1}^{4} 2(3^{n - 1})[/tex]
Substituting n = 1 , 2 , 3 and 4 in [tex] 2(3^{n - 1})[/tex] and then adding them , we have;
[tex]\implies s_4 = 2(3^{1-1}) + 2( 3^{2-1})+2(3^{3-1})+2(3^{4-1}) \\[/tex]
Take out 2 as common,
[tex]\implies s_4 = 2 [ 3^0 + 3^1 + 3^2 + 3^3]\\[/tex]
[tex]\implies s_4 = 2 [ 1 + 3 + 9 + 27 ] \\[/tex]
[tex]\implies s_4 = 2 ( 40) \\[/tex]
[tex]\implies \underline{\underline{ s_4 = 80}} \\[/tex]
Hence the required answer is 80 .
and we are done!
Work out the circumstances of this circle. take π to be 3.142 and give your answer to 1 decimal place. Radius is 4cm
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is pi, and r is the radius.
Substituting the given value of π = 3.142 and r = 4 cm, we get:
C = 2 x 3.142 x 4
C = 25.136 cm
Therefore, the circumference of the circle is 25.1 cm (rounded to 1 decimal place).