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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 less or equal to 10,000 (Sales demand for Product X)
y less or equal to 12,000 (Sales demand for Product Y)
5x + 4y less or equal to 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.
(a)What is the shadow price per direct labour hour and
(b)for how many additional hours of labour does this shadow price per hour apply?1. I do have calculated the shadow price which is $1.50.
2. For part (b), the answer is 38,000 hrs.
3.Could you explain what the question actually wants and how to obtain the answer?Thanks.
If they get more labour then they will make more Y’s (they cannot make more X’s because they cannot sell them).
However once they are making 12,000 Y’s then there is no point in buying any more labour because there would be no point in making more Y’s, so the shadow price of labour would then be zero.
12,000 Y’s would be making an additions 12,000 – 2,500 = 9,500 more Y’s, and this would use 9,500 x 4 = 38,000 more hours of labour.
Hi John,
I was wondering if you could be able to help me …..Just working on exam kit and I am a little unsure of how to deal with losses on materials and idle time for labour. For example if a product X needs 3kg of material A and 7kg of material B but a loss of .01kg in each material, how do I deal with this type of questions?
Many thanks,
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