A basketball team is planning to sell calendars as a...

Name: a basketball team is planning to sell calendars as a fundraiser the data from previous years suggests that when the price of the calendar is 15 they sell 80 calendars the coach believes that 22028
Uploaded: 2022-12-06T16:01:42-08:00
Duration: 5 min 36 s
Channel: Sri K
Description: a basketball team is planning to sell calendars as a fundraiser the data from previous years suggests that when the price of the calendar is 15 they sell 80 calendars the coach believes that 22028

A basketball team is planning to sell calendars as a fundraiser. The data from previous years suggests that when the price of the calendar is $15 they sell 80 calendars. The coach believes that for every $0.25 increment that the price is decreased, an additional two calendars will be sold. If R represents the revenue and x represents the number of price increments, then the quadratic function that represents this scenario is Select one: O a. R(x) = (15-0.25x)(80-2x) O b. R(x) = (15+0.25x)(80-2x) O c. R(x)=(15+0.25x)(80+2x) O d. R(x)= (15-0.25x)(80+2x)

Transcript

00:01 Hello, let's have a look at the question.

00:04 Now x is equal to number of television sold per week.

00:17 Now for the a part, let us take px is equals to a plus bx.

00:24 Now x is given to us 1 ,650 and p is equals to $540.

00:32 So now the equation will become a plus 1 .650.

00:36 650 b equals to 540 now let this be the first equation now x is equals to 1650 plus 240 and now pv is equals to 540 minus 24 so now the equation will become a plus 1650 plus 240 b is equal to 540 minus 24 so now the equation will become a plus 1650 plus 240 b is equal to 540 minus 24.

01:13 On solving this we will get a plus 1 890 b is equals to 516.

01:21 Now let this be the second equation.

01:23 Now we will subtract 1 and 2 so we will get minus 240 b is equal to 24 so from here the value of b is equals to minus 1 by 10.

01:38 Now let us put in first equation so we will get a minus 1650 divided by 10 is equals to 540 so from here we will get the value of a is equals to 705 hence we can say that px is equal to 705 minus 0 .1x now for the b part the revenue let rx is equal to x into px so this will be equals to 705x minus 0 .1x square.

02:20 Now let us calculate r -dash -x that is differentiation of revenue.

02:24 So we will get 705 minus 0 .2x.

02:30 Now let us put this equals to 0.

02:32 So from here we will get the value of x equals to 705 divided by 0 .2 which is equals to 3 ,525.

02:42 Now r double dash x is equals to minus 0 .2 which is less than 0.

02:52 So we can say that rx is maximum at x is equals to 3525.

03:01 Now let us calculate the value of p at 3 ,525.

03:05 So this will be equals to 705 minus 352 .5.

03:11 So this will be equals to 352 .5...