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A company makes two products x,y on the same type of direct labour hour and production capacity per period is restricted to 60000 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 <or = 10000 ( sale demand for x)
Y <or = 12000 (sale demand for y)
5x +4y <or= 60000(direct labour hours)
The contribution maximising output is to produce and sell 10000 unit of x and 2500 of y
What is shadow price per direct labour hour and how many additional hours of labour does this shadow price per hour apply.My question regarding why in the revision kit answer he just caculated y and didnt caculate x before multiplying it by the contribution per unit and also how did he get the 38000 hours.
Thank you in adavance i know have been asking alot of question lately but sometimes i cant seem to figure it out on my own.
Given that from the equations, the maximum demand for X is 10,000 units, then any additional hours can only be used to make Y (because at the current maximising output they are producing only 2,500 units of Y, but according to the equations the production of Y can be anything up to 12,000 units.
So, if they get more hours then they will be able to produce more units of Y, but since the maximum units of Y they can produce (from the second equation) is 12,000 units, then the maximum number of hours they will need is (10,000 x 5) + (12,000 x 4) = 98,000, which is 38,000 hours more than the current 60,000 hours that are available.
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