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explain how you know this is already in standard form

P = 2x + 4y
subject to constraints:
x + 4y <= 12
x + 3y <=10
x >= 0, y >= 0

"standard" form is usually ... Ax + By = C

... with A, B, and C being integer values (whole numbers)

Did you know?

Did you know that a linear programming problem is considered to be in standard form when the objective function is to be maximized and all variables are non-negative? In order to determine if a problem is in standard form, you need to check if the objective function is already written in terms of the variables with non-negativity constraints, denoted by x ≥ 0 and y ≥ 0. Additionally, the problem should include inequality constraints that restrict the values of the variables. For example, in the given problem, P = 2x + 4y is the objective function that needs to be maximized, while the constraints x + 4y ≤ 12 and x + 3y ≤ 10 restrict the possible values of x and y. Since all these criteria are met, we can conclude that the problem is already in standard form.