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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 than or equal to) 10000
y <=( less than or equal to) 12000
5x + 4y <=( less than or equal to) 60000
The contribution- maximising out put is to produce ans sell 10000 of X and 2500 of YWhat is the shadow price per direct labour hour and for how many additional hours of labour does this shadow price per hour apply ?
My question is while calculating shadow price why we can’t use y = 12000 for the equation , I tried but it Shows large difference
I can’t understand what you should want to use y = 12,000 – it would make no sense at all.
To calculate the shadow price of labour you calculate what the production would be if we had 1 extra hour of labour i.e. 60,001 hours of labour in total, and the shadow price is the extra contribution that would then be generated.
With 1 more hour we could produce more units, but we cannot produce more X’s because we are already producing maximum demand. Therefore we would produce more Y’s. Since each Y takes 4 hours of labour, then 1 extra hour would mean we could produce 0.25 more Y’s which would generate an extra 0.25 x $6 = $1.5 contribution. Therefore this is the shadow price.
I do suggest that you watch my free lectures on linear programming. My lectures are a complete free course for Paper F5 and cover everything needed to be able to pass the exam well.
Thank you so much for replying John , your second last paragraph made me clear for my confusion, even I learn shortcut way of calculating shadow price which I was not aware of , thanks again
I know how to calculate the shadow price of labour in this question. But how do we calculate the additional hours that this shadow price is applicable for?
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