A line has a slope of zero

A store has been selling 100 Blu-ray disc players a week at $600 each. A market survey indicates that for each $40 rebate offere

Sav [38]

Answer:

<em>The rebate should be $220</em>

Step-by-step explanation:

<u>Demand Curve</u>

It's the relationship between price (P) and quantity (Q) demanded a certain product or service.

(a) We need to find the function that relates both magnitudes assuming a linear equation. The equation of a line can be found with the point-point formula:

$\displaystyle Q-Q_1=\frac{Q_2-Q_1}{P_2-P_1}(P-P_1)$

Two sets of data are given: 100 Blu-ray disc players are sold a week at $600 each. The ordered pair for this condition is (P,Q)=(600,100).

The other point comes from the market survey: The number of units sold will increase by 80 (100+80=180) when the price goes down $40 (600-40=560). The new point is (P,Q)=(560,180)

We set up the equation of the demand

$\displaystyle Q-100=\frac{180-100}{560-600}(P-560)$

Rearranging

$-40Q+4000=80P-44800$

Or

$80P+40Q=48800$

Simplifying

$2P+Q=1120$

(b) The revenue function is Q times the price

$R=Q.P$

Solving the equation of the demand for P

$\displaystyle P=\frac{1120-Q}{2}$

Thus, the revenue is

$\displaystyle R=Q\cdot \frac{1120-Q}{2}$

$\displaystyle R=\frac{1120Q-Q^2}{2}$

(c) To find the optimum value of the revenue, we take the derivative of R and equate to 0

$\displaystyle R'=\frac{1120-2Q}{2}=560-Q=0$

Solving

Q=560 units a week

For which the revenue is

$\displaystyle R=\frac{1120(560)-560^2}{2}$

$R=\$156,800$

And the price is

$\displaystyle P=\frac{1120-560}{2}=280$

$P=\$280$

The rebate should be $600-$280=$220

4 0

3 years ago

Steven must save $240 to attend summer camp next year. He already saved $30 if you earns $14 per week how many weeks must he sav

Anarel [89]

Answer:

11 2/3

Step-by-step explanation:

240-30

210

210/18

11

3 0

3 years ago

A chocolate factory makes 6060 chocolates in an hour .How many chocolates can it make in a day , if the factory is operational f

dimulka [17.4K]

Answer:

78,780

Step-by-step explanation:

Given:

6060 chocolates made per hour
13 hours in one day

Number of chocolates made in 1 day = number of chocs/hr × number of hours

= 6060 × 13

= 78,780

6 0

2 years ago

If g(x) = 2x^2 - 4x, what is the value of g(- 2)?

svlad2 [7]

Answer:

Hi! The correct answer is -8 - 4x!

Step-by-step explanation:

Simplify each term

6 0

3 years ago

Perform the indicated operation. Be sure the answer is reduced.

Morgarella [4.7K]

The answer is: $k^{2} /2
$
The explanation is shown below:
1. You have the following expression given in the exercise above:
$( 4k^{2}) /(2k+3)(2 k^{2} -5k-12)/(8k-32)
$
2. By applying the distributive property, you obtain:
$(8k^{4}-20k^{3}-48k)/(16k^{2} -40k-96)$
3. Now, you must factor $k^{2}$ in the numerator and $2
$ in the denominator:
$k^{2}(8 k^{2} -20k-48)/2(8 k^{2} -20k-48)$
4. Simplify:
$k^{2} /2$

8 0

3 years ago