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

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 the number of hours is represented by h and has the constraints. 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 the number of hours is represented by h and has the constraints. complete the sentences to represent the constraints on the variables.

Answer

Explanation:

Step1: Identify the variable constraints

The number of hours $h$ that laborers can work. They can work up to a full - 8 - hour work day, so $0\leq h\leq8$.

Step2: Analyze the profit function constraints

The profit function is $P(h)=6362-(5254 + 45.75h)$. The profit $P(h)$ must be non - negative. First, simplify the profit function: $P(h)=6362 - 5254-45.75h=1108 - 45.75h$. For $P(h)\geq0$, we solve the inequality $1108 - 45.75h\geq0$.

Answer:

$0\leq h\leq8$; $0\leq P(h)\leq1108$