00:01
Hello, in this problem we are given the cost and the revenue functions.
00:11
And we have several questions to answer.
00:16
So the first one is under a.
00:18
When q is equal 500, when we have 500 units produced, what is the cost, what is the revenue? can we sell 500 units and do we have a profit? okay, let's calculate how much c of 500 is.
00:34
We replace q with 500, so it's 6 ,000 plus 10 times 500, which is 6 ,000 plus 5 ,000, which is 11 ,000.
00:50
The revenue of selling 500 products is 12 times 500 products, which is 60 with $2 ,000, dollars.
01:07
The profit function is defined as the revenue minus the costs when the costs are greater the revenue than the revenue then we have a negative profit so the profit is minus five thousand dollars and in other words we incur no profit the company incur is no profit.
01:37
There is a loss of $5 ,000 when a quantity of 500 units is produced.
01:52
Now, what happens when the number of units is 5 ,000? c of 5 ,000 equals 6 ,000 plus 10 times 5 ,000, which is 6 ,000 plus 50.
02:12
It's $56 ,000.
02:17
The revenue of 5 ,000 items sold is 12 times 5 ,000, which is 12 times 5 is 60 with these 3 zeros is 60 ,000.
02:30
Now we have a profit of 60 ,000 minus 56 ,000, which is plus $4 ,000.
02:45
We have profit.
02:48
We have a profit.
02:51
So, producing and selling 500 pieces, inker's costs of 11 ,000, a revenue 6 ,000, and the loss of 5 ,000.
03:05
The costs involved in producing 5 ,000 units of $56 ,000.
03:11
The revenue is $60 ,000 by selling 5 ,000 units, by which we make a profit of $4 ,000.
03:21
Okay.
03:22
We now go to question b.
03:25
What is the breaking point and to give a graphical interpretation.
03:33
The break -even point is the quantity q for which we have that the revenue of q, revenue of selling q items, is the same as the cost of producing q items incurring a profit of zero.
04:04
That is neither a profit nor a loss.
04:08
So we equate 12q with cfq, which is 6 ,000 plus 10 q.
04:19
Subtracting 10 q from both sides, 12 minus 10 is 2q equals 6 ,000.
04:26
Divide by 2, we have q equals 3 ,000 units produced.
04:37
Now, at 3 ,000 units produced, we have the revenue of 3 ,000, which is the same as cost of 3 ,000 produced is the simple one is this one, so it's 12 times 3 ,000, which is $36 ,000 is the revenue gained by selling 3 ,000 units, and it equals the cost of producing 3 ,000 units...