The correct answer is: 460 x and 200 y.

Solve simultaneous equations to find 'outer' point of the feasible region.

10x + 7y = 6,000 (I)

5x + y = 2,500 (II)

Multiply II by 2

10x + 2y = 5,000

Subtract from I to give

5y = 1,000

y = 200

Substitute for y in I to find x

10x = 6000 - 7 (200)

10x = 4600

x = 460

At x = 460, y = 200, contribution = 50 (460) + 30 (200) = $29,000

[Check other 'outer' points of feasibility region

10x + 7y = 6,000 : if x = 0, y = 857, if y = 0, x = 600

5x + y = 2,500 : if x = 0, y = 2,500, if y = 0, x = 500

So the other 'outer' points are x = 0, y = 857 with contribution = $25,710

and y = 0, x = 500 with contribution = $25,000]