00:01
If a small business makes cookies and sells them at the farmer's market and the fixed monthly cost for the use of the health department approved kitchen and rental space at the farmer's market is 790.
00:12
So we're going to jot down all of the information we're going to need.
00:16
The cost, labor, and taxes and the ingredients for the cookies comes out to 24 cents per cookie.
00:27
And the cookies sell for $6 per dozen.
00:31
And there's 12 cookies and a dozen, so it's $6 per 12 cookies.
00:36
Next, we're going to write a linear cost function representing the cost to produce x dozen cookies per month.
00:43
So we get the cost equals the number of cookies, 0 .24 times x the number of cookies, plus that $790 flat fee.
00:54
So that's our cost function to produce a given number of cookies.
00:59
Next, we're going to write a profit function that represents the profit for reducing and selling x dozen cookies in a month.
01:07
So we get the profit is 0 .5x, 50 cents per cookie times x.
01:17
That 50 cents comes from right here.
01:19
It's $6 per 12 cookies.
01:23
So $6 per 12 cookies, which is one half or 0 .5.
01:28
And that gives me the cost or the cost of the cookie per cookie that they're charging to buy a cookie.
01:35
And i want to be consistent.
01:36
So since this was per cookie, i want this to be per cookie as well.
01:42
Next, we're going to write a profit function representing the profit for selling and making a certain number of cookies.
01:52
And we get that the profit of the cookies is the revenue function minus the cost function.
02:03
So we get the profit of the cookies is 0 .5x minus 0 .24x minus 790.
02:13
The profit, therefore, we're going to combine like terms and we get 0 .26x minus 790.
02:22
Now we're going to figure out the number of cookies in dozens that need to be produced and sold for a monthly profit.
02:29
Okay, so i want to make money.
02:32
So we're going to set the profit equal to zero.
02:40
So we're going to get 0 equals 0 .26x minus 790.
02:45
Now we're going to solve for x, add 790.
02:48
To both sides.
02:52
I get 790 equals 0 .2x divided by 0 .26...