To determine the objective function, we need to formulate the total cost [tex]\(C\)[/tex] of running machine [tex]\(X\)[/tex] and machine [tex]\(Y\)[/tex] for [tex]\(x\)[/tex] hours and [tex]\(y\)[/tex] hours, respectively.
Given:
- The cost to run machine [tex]\(X\)[/tex] is [tex]$22 per hour.
- The cost to run machine \(Y\) is $[/tex]25 per hour.
We can now express the total cost [tex]\(C\)[/tex] in terms of [tex]\(x\)[/tex] (hours machine [tex]\(X\)[/tex] runs) and [tex]\(y\)[/tex] (hours machine [tex]\(Y\)[/tex] runs).
The cost [tex]\(C\)[/tex] can be formulated as follows:
[tex]\[
C = 22x + 25y
\][/tex]
Thus, the objective function is:
[tex]\[ C = 22x + 25y \][/tex]
So, the objective function [tex]\(C\)[/tex] in its complete form with the specified coefficients for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] is:
[tex]\[ C = 22x + 25y \][/tex]
Therefore, the objective function is [tex]\( C = 22x + 25y \)[/tex].
