What is the minimum value of cap c is equal to 7 x plus 8 y , given the constraints on x and y listed? 2 x plus y is greater than or equal to 8 x plus y is greater than or equal to 6 x is greater than or equal to 0 y is greater than or equal to 0

Because x and y are nonnegative, check the boundary where y = 0. The constraints then require 2x ≥ 8 and x ≥ 6, so the smallest feasible x is 6. This gives C = 7(6) + 8(0) = 42. The point (6, 0) satisfies both constraints, so the minimum is 42, choice B.

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