What is the maximum value of cap p is equal to 4 x plus 2 y , given the constraints on x and y listed? x plus 2 y is less than or equal to 10 y is less than or equal to 2 x is greater than or equal to 0 y is greater than or equal to 0

The constraints include x + 2y ≤ 10, with x and y nonnegative. Since y ≥ 0, the first constraint gives x ≤ 10, so 4x + 2y ≤ 40 + 2y; more directly, using x ≤ 10 − 2y gives 4x + 2y ≤ 40 − 6y ≤ 40. The maximum is reached at x = 10 and y = 0, which satisfies all the constraints, so the maximum value is 40, choice B.

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