00:01
Hi, given the revenue function r of x is equal to 45x, also given the total cost function c of x is equal to 2 ,200 plus 25x plus 0 .01 into x square.
00:25
First, we know the profit function p of x is given by revenue function.
00:39
Minus cost function.
00:43
This implies we have p of x is equal to revenue function is 45x minus cost function is 2 ,200 plus 25x plus 0 .01 x this implies we have p of x is equal to minus 2 ,200 plus 20 x minus 0 .01 x square.
01:14
Now, substituting 500 in place of x, we get p of 500 is equal to minus 2 ,200 plus 20 into 500 minus 0 .01 into 500 square.
01:32
On simplifying this we get this value is equal to 5 ,300.
01:44
Profit from the production and sale of 500 units is given by p of 500 is equal to dollar 5 ,300.
01:59
Next we need to find marginal profit function.
02:11
Marginal profit function is given by p dash of x therefore we have marginal profit function is equal to differentiating profit function we have 20 minus 0 .01 into 2 x therefore marginal profit function is given by 20 minus 0 .02.
02:47
Next, we need to find the marginal function value at x is equal to 500.
02:58
Substituting 500 in place of x we get marginal profit function is equal to 20 minus 0 .02 into 500...