00:01
In this problem, it is said that a manufacturer has a monthly fixed cost of $40 ,000 and a production cost of $8 for each unit produced.
00:09
The product sells for $12 a unit.
00:12
And the first subpart, we have been asked, what is the cost function? so we represent the cost function as c of x, where x represents the number of units.
00:24
So there is a monthly fixed cost of $40 ,000.
00:29
And along with this there is a cost of $8 for each unit produced so for x units produced the cost will be 8x so the cost function is 40 ,000 plus 8x in the next subpart we have been asked what is the revenue function we represent the revenue function as r of x and it is said that the product sells for $12 a unit so the revenue will be 12 times the number of units sold that is 12x next, we have to determine the profit function.
01:02
We represent the profit function as p of x, and the profit function is the revenue function minus the cost function.
01:10
Now, the revenue function is 12x, and we subtract from that the cost function, that is 40 ,000, plus 8x.
01:22
So we end up with 12x minus 40 ,000 minus 8x.
01:29
12x minus 8x is 4x, and we have 4x minus 40.
01:34
Thousand.
01:35
So this is the required profit function.
01:41
And in the next sub part, we have been asked to determine the profit or loss corresponding to the production levels of 8 ,000 and 12 ,000 units.
01:50
So first of all, for 8 ,000 units, we need to determine p of 8 ,000...