Linear programming

Q) A company makes two products, X and Y, on the same type of direct labour, and production capacity per period is restricted to 60,000 direct labour hours. The contribution per unit is $8 for Product X and $6 for Product Y. The following constraints apply to production and sales: x < 10,000 (Sales demand for Product X) y < 12,000 (Sales demand for Product Y) 5x + 4y < 60,000 (Direct labour hours) The contribution-maximising output is to produce and sell 10,000 units of Product X and 2,500 units of Product Y. What is the shadow price per direct labour hour and for how many additional hours of labour does this shadow price per hour apply? A $1.50 per hour for the next 38,000 direct labour hours B $1.50 per hour for the next 47,500 direct labour hours C $1.60 per hour for the next 38,000 direct labour hours D $1.60 per hour for the next 47,500 direct labour hours Answer: A The correct answer is: $1.50 per hour for the next 38,000 direct labour hours. If one extra direct labour hour is available, the optimal solution will change to the point where: (1): sales demand for X: x = 10,000 (2): direct labour 5x + 4y = 60,001 Multiply (1) by 5 (3) 5x = 50,000 Subtract (3) from (2) 4y = 10,001 y = 2,500.25 Now Total contribution = $(10,000 × $8) + $(2,500.25 × $6) = $80,000 + $15,001.15 = $95,001.50 Total contribution in original solution = $(10,000 × $8) + $(2,500 × $6) = $95,000 The shadow price per direct labour hour is therefore $1.50. The solution is changing because each additional labour hour allows the company to produce an additional 0.25 units of Product Y, to increase total contribution by $1.50. This shadow price will cease to apply when the direct labour hours constraint is replaced in the optimal solution by the sales demand for Product Y constraint. At this level of output, total labour hours would be (10,000 units of X at 5 hours) + (12,000 units of Y at 4 hours) = 98,000 hours. The shadow price of $1.50 per hour therefore applies for an additional 38,000 hours above the current limit. i dont understand why has x = 10,000 been taken as the starting point for the optimal solution, as opposed to y = 12,000. if i choose y = 12,000 gives the apparently incorrect answer of $1.60 per hour.