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A company makes two products, X and Y, using the same type of direct labour. 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?i couldn’t understand how they come to solution of 38000 direct labour hours
The shadow price per direct labour hour is $1.50. This shadow price per hour applies for an additional 38,000 direct labour hours.
To work it out, you can use the concept of shadow prices in linear programming. The shadow price represents the change in the objective function value for each additional unit of a resource. In this case, the shadow price per direct labour hour is $1.50, which means that for each additional hour of labour, the total contribution will increase by $1.50.
This shadow price per hour applies as long as the direct labour hours constraint is not replaced by the sales demand for Product Y constraint.
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