00:01
Hi there, so for this problem we're told that a company manufactures and sells x forms per week.
00:08
Now we're given that the price for this is 500 minus 0 .5 times x and the cost function for this is 15 000 this plus 140 times x.
00:26
So the question for part a of this problem is about what price should the company charge for the forms and how many firms should produce to maximize the weekly revenue.
00:37
So first of all remember that the revenue is just the pair between x and the price so that will be just simply 500 times x minus 0 .5 times x squared.
00:48
Now in order to minimize this, well to maximize the revenue we are going to derivate this with respect to x and set that equal to zero.
00:57
So that will be 500 minus x and then we set this equal to zero.
01:04
Then solving for x that will be 500.
01:06
So this is the amount of funds that we need to sell.
01:10
So the company should produce 500 funds, each will cost, so we now substitute that in here, so the price for each fund is 500 minus 0 .5 times this value.
01:26
So this will give us 250.
01:29
So that is the price for each fund and finally with this we can obtain the maximum weekly revenue because we just evaluate the revenue at this value.
01:40
So the revenue at this value is equal to 500 times 500 and then this minus 0 .5 times 500 to the square.
01:57
So then using our calculator we obtain a value of 125 ,000.
02:16
So that is the maximum revenue.
02:21
Now for the next question in part b of this problem we are told what price should the company charge for the funds and how many funds should be produced to maximize the weekly profit.
02:34
So in this case remember that the profit is just the revenue minus the cost...