The correct answer is: $4.

The overtime premium is the shadow price of labour i.e. the amount by which contribution increases if one extra hour of labour becomes available.

Solve simultaneous equations to find the '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 so 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 the feasibile 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]

So, with 6,000 hours of labour, the maximum contribution is $29,000. With one extra hour, the constraints become:

10x + 7y = 6,001 (I)

5x + y = 2,500 (II)

Multiply II by 2: 10x + 2y = 5,000

Subtract from I to give: 5y = 1,001 y = 200.2

Substitute into I to find x

10x = 6,001 – 7(200.2)

10x = 6,001 – 1,401.4

10x = 4,599.6

x = 459.96

Contribution is now: 50 (459.96) + 30 (200.2) = $29,004

Contribution was: $29,000

Shadow price is $4