To determine what needs to be sold to make a profit greater than $150, the owner writes the function 2 + 3 < 150.
Let's break this down step by step:
1. The variable "b" represents the number of hamburgers sold, and the variable "d" represents the number of hotdogs sold.
2. The function 2 + 3 represents the cost of selling each hamburger and hotdog. The cost of a hamburger is $3, and the cost of a hotdog is $2. So, the total cost of selling one hamburger and one hotdog is $3 + $2 = $5.
3. The function 2 + 3 < 150 is used to determine what combination of hamburgers and hotdogs needs to be sold in order to make a profit greater than $150. In other words, the owner wants to find the values of "b" and "d" that satisfy this inequality.
To solve this inequality, we need to rearrange it:
2 + 3 < 150
5 < 150
Now, let's interpret this inequality:
The sum of the costs of the hamburgers and hotdogs needs to be less than $150 in order for the owner to make a profit greater than $150. This means that the revenue from selling the hamburgers and hotdogs should be greater than the cost of supplies, which is $150.
For example, if the owner sells 25 hamburgers and 10 hotdogs, the revenue would be (25 * $3) + (10 * $2) = $75 + $20 = $95. Since $95 is less than $150, the owner would make a profit greater than $150.
In summary, the owner needs to sell a combination of hamburgers and hotdogs such that the revenue is greater than the cost of supplies ($150) to make a profit greater than $150. The specific values of "b" and "d" will depend on the prices and quantities sold, but the total revenue needs to exceed $150.