00:01
In this problem, it is said that in a certain company, the materials and labor costs for making a product is $200, and the fixed cost per week is $12 ,000.
00:11
Now, the selling price for each product is $500, and if the company sells 50 units, then we need to determine the total profit for the company.
00:20
So, first of all, let us consider the cost function, c of x.
00:24
Now, the cost function is equal to the fixed cost, which is 12 ,000, plus the variable cost.
00:35
And the cost for making one product is 200.
00:38
So the cost for making x products will be 200x.
00:42
So the cost function is equal to the fixed cost plus the variable cost, and so this is what we get.
00:50
Next, let us determine the revenue function.
00:53
Now, the revenue function is obtained by multiplying the selling price, which is $500, by the number of products, which is x.
01:03
So the revenue function is 500x, meaning that the revenue obtained on selling x products is $500x.
01:11
Now, the profit function, p of x, this profit function is given by r of x minus c of x.
01:20
So r of x is 500x.
01:24
And from that we subtract c of x, which is 12 ,000 plus 200 x...