A marketing expert determines that sales of television sets an be increased by 3 sets per week for each $20 decrease in price. Weekly sales average 18 sets at $440 each. What price should be given in order to receive $10,800 in revenue?
(18+3x)(440-20x)=10800
We get, -60x^2 + 960x - 2880 = 0;
Using Quadratic Equation, we have x= 12 or 4; Price = (440-20x); We have 440-80 or 440-240; We get $360 or $200 as the price.
thank you
To determine the price that should be given in order to receive $10,800 in revenue, we can follow these steps:
Step 1: Calculate the current revenue per week.
Revenue per week = Weekly sales * Price per set
Revenue per week = 18 sets * $440
Revenue per week = $7920
Step 2: Determine the increase in sales per week for each $20 decrease in price.
Increase in sales per week = 3 sets
Step 3: Calculate the decrease in price needed to achieve the desired increase in sales.
Decrease in price needed = desired increase in sales / increase in sales per week
Decrease in price needed = $10,800 / 3 sets
Decrease in price needed = $3600
Step 4: Calculate the new price.
New price = Current price - Decrease in price needed
New price = $440 - $3600
New price = $4040
Therefore, the price that should be given in order to receive $10,800 in revenue is $4040.
To determine the price that will generate $10,800 in revenue, we need to find the number of sets that will be sold at that price.
Let's assume the price we are trying to find is x (in dollars). We know that for each $20 decrease in price, sales increase by 3 sets per week.
This means that for every $20 decrease in price, the number of sets sold per week increases by 3. We can calculate the difference between the actual price ($440) and the price we are trying to find (x) using the formula:
Difference in price = ($440 - x)
We can then calculate the number of sets sold per week by multiplying the difference in price by the rate of increase in sales:
Number of sets sold per week = (Difference in price / $20) * 3
Now, we have all the information we need to calculate the revenue generated from selling the sets:
Revenue = Number of sets sold per week * Price per set
Given that the weekly sales average is 18 sets at $440 each, we can substitute these values into the equation to find a relationship between the price and revenue:
18 * $440 = (Difference in price / $20) * 3 * x
To find the price (x) that will generate $10,800 in revenue, we need to solve the equation:
10,800 = (Difference in price / $20) * 3 * x
Let's plug in the actual values and solve for x:
10,800 = (($440 - x) / $20) * 3 * x
Now, we can proceed to solve for x:
First, let's get rid of the fraction by multiplying both sides of the equation by $20:
216,000 = (440 - x) * 3 * x
Next, let's distribute the terms:
216,000 = (1320x - 3x^2)
Now, let's rearrange the equation to be a quadratic equation:
3x^2 - 1320x + 216,000 = 0
To solve this equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 3, b = -1320, and c = 216,000.
Plugging in the values, we get:
x = (-(-1320) ± sqrt((-1320)^2 - 4 * 3 * 216,000)) / (2 * 3)
Simplifying further:
x = (1320 ± sqrt(1,742,400 - 2,592,000)) / 6
x = (1320 ± sqrt(-849,600)) / 6
Since the value inside the square root is negative, it means that there are no real solutions to this equation. Therefore, there is no price (x) that will result in a revenue of $10,800 with the given conditions.
In other words, it is not possible to achieve a revenue of $10,800 given the current pricing and sales structure.