To determine the objective function, we need to consider the cost of running each machine per hour and how many hours each machine runs.
Let's break down the data provided:
- Machine [tex]\(X\)[/tex] requires 4 units of [tex]\(A\)[/tex] and 5 units of [tex]\(B\)[/tex] per hour and costs \[tex]$22 per hour to run.
- Machine \(Y\) requires 3 units of \(A\) and 10 units of \(B\) per hour and costs \$[/tex]25 per hour to run.
- Let [tex]\(x\)[/tex] be the number of hours machine [tex]\(X\)[/tex] runs.
- Let [tex]\(y\)[/tex] be the number of hours machine [tex]\(Y\)[/tex] runs.
The objective function is the total cost [tex]\(C\)[/tex] to run the machines, which can be expressed as a linear combination of the costs of running each machine.
The cost to run machine [tex]\(X\)[/tex] for [tex]\(x\)[/tex] hours is [tex]\(22x\)[/tex].
The cost to run machine [tex]\(Y\)[/tex] for [tex]\(y\)[/tex] hours is [tex]\(25y\)[/tex].
Thus, the objective function [tex]\(C\)[/tex] representing the total cost is:
[tex]\[C = 22x + 25y\][/tex]
So, the completed objective function is:
[tex]\[C = 22x + 25y\][/tex]
Therefore, the objective function can be written as:
[tex]\[C = 22x + 25y\][/tex]
In summary:
- The coefficient of [tex]\(x\)[/tex] (representing hours machine [tex]\(X\)[/tex] runs) is 22.
- The coefficient of [tex]\(y\)[/tex] (representing hours machine [tex]\(Y\)[/tex] runs) is 25.
Thus, [tex]\(C = 22x + 25y\)[/tex].
