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- Machine [tex]\(X\)[/tex]: 4 units of [tex]\(A\)[/tex] and 5 units of [tex]\(B\)[/tex] per hour
- Machine [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 per hour
- Cost to run machine \(Y\): \$[/tex]25 per hour

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 [tex]\(C = \square x + \square y\)[/tex].



Answer :

GinnyAnswer
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].

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