Your company produces computers each month in a given month...

Your company produces computers each month. In a given month, the company has fixed costs of $115,000, and it costs an additional $468 to produce each computer. If the company sets the price to be $1000 per computer, it can sell 2200 computers. It can only sell 2100 computers if it raises the price to $1280 per computer. What price should the company charge in order to maximize profit? Assume linear demand. The company should charge a price of ... dollars per computer. If necessary, round to two decimal places. Do not include units.

Transcript

00:01 Hello, in this question we are given that the fixed post for the company to produce computers is 1 ,15 ,000 and the variable cost is 468 per computer, okay? and if the price is 1000 per computer, it can sell 2 ,200s.

00:30 If the price is 1000, it can sell 2 ,200 computers.

00:40 20, 200.

00:44 And if the price is 1028, it can sell only 2100 computers.

00:51 Okay, now we need to calculate what will be the maximum number of computers to be sold so that the profit is maximum.

01:06 Okay, so what we will do is we will generate a function as a assuming value x number of units sold okay and then we will differentiate the then we will check at what value it will come out to be maximum okay so there in the state line can be written as for one zero to eight it is 2100 and for thousand it is 2200 so the line can be written as y minus 2200 over 1 280 minus 1000 is equal to x minus 1000 is it correct sorry this will come off to this will be 21 minus 2200 okay this will be the equation.

02:44 Of the line so it is simplify this what we will get is y why is number of units sold sorry this is not x this is y so the y is number of units sold it will get a it's equal to minus hundred divided by 280 into x minus 100 sorry thousand over 280 plus 2200 okay we will get it something like this or not just a second let me recheck the calculations in 200 i think it will come out to be 100 yes let me read it okay so the value will come out to be minus 100 this minus over this side minus 100 over 280 and minus thousand into minus 100 over 280 and this 2 200 will be plus 220 okay so the value when simplified will come out to be y is equal to minus 5 over 14 x plus let me calculate this value 2200 plus 1000 plus 1000 to 200 plus over 20.

04:46 So it will come out to be 2557 .14.

04:52 So y as a function of x is given by this.

04:58 So cost means x and number of units sold is y.

05:03 So the total profit will be, profit will be number of units sold that is y multiplied by the rate at it is sold minus the variable cost that was 468 x8 minus 1 .151 into y number of being sold minus 1 lakh 15 ,000.

05:33 This will be the profits.

05:35 So when we simplify this but we get let me write it again p is equal to minus 5 over 14 x square plus 2557 .14 xxx okay minus 468 into minus 5 by 14 x plus 468 into 2557 .14.

06:05 X plus 468 into 2557 .14.

06:11 Minus 11500 triple zero.

06:14 So when further simplified it will come out to be minus 5 over 14 x square plus let me solve it plus 468 into 5 by 14.

06:27 It will be 2724 .29x plus 468 into 2557 .17 .14 .14 minus 115 .2.

06:46 It will come out to be 1 .8174 .1 .52 .2.

06:53 Okay.

06:54 So when further sold, from here we will calculate maximum value of p.

07:00 For that dp over d x must be equal to 0.

07:05 So, minus 10 over 14x plus 27 to 4 .29x...