Suppose that a when a cell phone store charges 16$ for a car charger, it sells 92 units. When it drops the price to 15$ it sells 96 units. Assume that demand is a linear function of price. If each phone charger costs 1$ to make, what price should the store charge to maximize its profit?
If x is the number of times the price is reduced by one dollar.

Find a function for total profit with respect to x. A negative value for x will mean the price is increased.

Answers

Answer 1

Answer: D(x) = mx + c ; where x is selling price , c is constant, m is slope
given D = 21 when x = $16
21 = 16m + c ------------1) and also we know D = 24 unit, when x = $15,
24 = 15m + c ------------2)
subtract eqn 2) from eqn 1) we get
-3 = m , and plug this value of m in eqn 1) we get
21 = 16*(-3) + c => c = 69
hence demand function
D(x) = -3x + 69
Cost price is C = $1
Profit = Revenue - Cost price
P(x) = Demand*Selling price - Cost per unit* Demand
P(x) = (69 - 3x)*x - 1*(69 - 3x)
P(x) = 69x - 3x² - 69 + 3x ; or
P(x) = - 3x² + 72x - 69 -------------Answer
Differentiate profit function with respect to x (selling price)
dP/dx = -3*2x + 72 - 0
0 = 72 - 6x ; plug dP/dx = 0 for maxima minima
6x = 72
x = $12 per unit --------Answer
(Since d²P/dx² = -6 < 0 , hence profit will be maximum at x = $12 per unit
and Demand would be D(@12) = 33 unit
Revenue = 33*$12 = $396
Cost = $1*33 = $33
Max Profit = #396 - $33 = $363

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Sue bought ten items at an average price of $3.60. The cost of eight of the items totaled $30. If the other two items were the same price, what was the price she paid for each ?1) $15, 2) $7.50, 3) $6, 4) $3, 5) $1.50

I guess the answer is $7.50.
What is yr answer ???

Answers

$(30+2x)/(10)=3.60\ \ \ \ /\cdot10\n\n30+2x=36\ \ \ \ /-30\n\n2x=6\ \ \ /:2\n\nx=3\ (\$)$

$Answer:\$3\ (4)$

ok soo if the 10 items avg $3.60 each then your total for the ten items was $36. if we know that the cost of 8 items is $30 then there is 6 dollars left. nd if we no that the remaining 2 are the same price then each should be $3

I need help please….

Answers

The solution to the equation 14h = 98 is h = 7.

To solve for h in the equation 14h = 98, we can divide both sides of the equation by 14. This gives us:

h = 98 / 14

h = 7

Therefore, the solution to the equation 14h = 98 is h = 7.

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Convert these base five and base two numbers to base ten.
a. 1312ve
b.110110110two

Answers

I am assuming A is base 5 based on the ve

a. 1*5^3 + 3*5^2 + 1*5^1+ 2*5^0
125+75+5+2

a = 207

b. 2+4+16+32+128+256

b = 438

(please note that a binary number having 9 digits is highly unusual. most are normally 8 which makes up a bit)

In triangle ABC, angle A measures 33 degrees and angle C measures 122 degrees. What is the measure of angle B?

Answers

Answer:

∠ B = 25°

Step-by-step explanation:

the sum of the three angles in a triangle = 180° , that is

∠ A + ∠ B +∠ C = 180° ( substitute values for A and C )

33° + ∠ B + 122° = 180° , that is

155° + ∠ B = 180° ( subtract 155° from both sides )

155° - 155° + ∠ B = 180° - 155° , that is

∠ B = 25°

Why is 0.3 a rational number A. It is on the number line.
B. The number can be written as a ratio of two integers.
C. It is a decimal.
D. The numbers can not be written as a ratio of two integers.

Answers

The number 0.3 is defined as a rational number, because: B. "The number can be written as a ratio of two integers."

What is a rational number?

A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.

The correct answer is B. "0.3" is a rational number because it can be written as the fraction 3/10, where the numerator (3) and denominator (10) are both integers since a rational number is defined as any number that can be expressed as the quotient or ratio of two integers, with the denominator not being zero.

In this case, 0.3 can be written as the ratio 3/10, making it a rational number. Therefore, the correct answer is option B.

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Answer : B. The number can be written as a ratio of two integers.

Explanation : In mathematics, a rational number is any number that can be expressed as a ratio of two integer numbers, being a non-zero denominator.

0.3 can be written as 3/10

$\textit{\textbf{Spymore}}$

What is the value of w in the equation 1/2w+7=2w-2

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$(1)/(2)w+7=2w-2\ \ \ \ |subtract\ 7\ from\ both\ sides\n\n(1)/(2)w=2w-9\ \ \ \ |subtract\ 2w\ from\ both\ sides\n\n-1(1)/(2)w=-9\n\n-1.5w=-9\ \ \ \ |divide\ both\ sides\ by\ (-1.5)\n\n\boxed{w=6}$

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