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- [tex]\(X\)[/tex]: 4 units of [tex]\(A\)[/tex] and 5 units of [tex]\(B\)[/tex] per hour
- [tex]\(Y\)[/tex]: 3 units of [tex]\(A\)[/tex] and 10 units of [tex]\(B\)[/tex] per hour
- Cost to run machine [tex]\(X\)[/tex]: [tex]\(\$22 / \text{hr}\)[/tex]
- Cost to run machine [tex]\(Y\)[/tex]: [tex]\(\$25 / \text{hr}\)[/tex]

[tex]\(x =\)[/tex] number of hours machine [tex]\(X\)[/tex] runs
[tex]\(y =\)[/tex] number of hours machine [tex]\(Y\)[/tex] runs

The objective function is [tex]\(C =\)[/tex] [tex]\(\square\)[/tex] [tex]\(x +\)[/tex] [tex]\(\square\)[/tex] [tex]\(y\)[/tex].

Sagot :

GinnyAnsweridn
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].
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