question 1 - 14 dontavious owns an air conditioning service company. he charges a customer $6,362 for a new…

question 1 - 14 dontavious owns an air conditioning service company. he charges a customer $6,362 for a new ac unit to be installed. it costs dontavious $5,254 for the unit and $45.75 per hour for his laborers. his laborers can work up to a full 8 - hour work day while installing the ac unit. the equation p(h)=6,362-(5,254 + 45.75h) represents dontavious profit for installing the ac unit. the profit is represented by p(h) and has the constraints of 8 ≤ p(h) ≤ 742. the number of hours is represented by h and has the constraints of 742 ≤ h ≤ 1108. complete the sentences to represent the constraints on the variables.

question 1 - 14 dontavious owns an air conditioning service company. he charges a customer $6,362 for a new ac unit to be installed. it costs dontavious $5,254 for the unit and $45.75 per hour for his laborers. his laborers can work up to a full 8 - hour work day while installing the ac unit. the equation p(h)=6,362-(5,254 + 45.75h) represents dontavious profit for installing the ac unit. the profit is represented by p(h) and has the constraints of 8 ≤ p(h) ≤ 742. the number of hours is represented by h and has the constraints of 742 ≤ h ≤ 1108. complete the sentences to represent the constraints on the variables.

Answer

Explanation:

Step1: Identify the variable constraints for hours

The laborers can work up to an 8 - hour work - day. So the number of hours $h$ has a lower bound of 0 (since you can't work negative hours) and an upper - bound of 8. So, $0\leq h\leq8$.

Step2: Identify the variable constraints for profit

We are given the profit function $P(h)=6362-(5254 + 45.75h)$. To find the bounds of the profit, we first consider the minimum and maximum values of $h$. When $h = 0$: $P(0)=6362-(5254+45.75\times0)=6362 - 5254=1108$. When $h = 8$: $P(8)=6362-(5254+45.75\times8)=6362-(5254 + 366)=6362 - 5620 = 742$. So, $742\leq P(h)\leq1108$.

Answer:

The constraints on the variables are $0\leq h\leq8$ and $742\leq P(h)\leq1108$.