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in question 89 publisher calculated the value of product y only and substituted in the equation of contribution but on the other hand in question 90 publisher calculated the value of both x and y could you explain the difference
I cannot help you because in the current edition of the BPP Revision Kit, question 89 only refers to Product X (there is no other product) and question 90 has nothing to do with individual products (there is no product X nor product Y).
a company makes 2 products x and y on the same type of direct labour 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 < 10000
y< 12000
5x+4y < 60000
the contribution maximising output is to produce and sell 10000 units of product x and 2500 units of product y.
what is the shadow price per direct labour hour?question 90
in a linear programming problem to determine the contribution maximising production and sales volumes for two products x and y the following information is available
product x product y total available
per unit per unit per period
direct labour hrs 2 hrs 4 hrs 10000 hrs
material x 4 kg 2 kg 14000 kg
contribution per unit $12 $18
the profit maximising level of output sales is 3000 units of product x and 1000 units of product y. what is shadow price of a direct labour hourFirst question:
Given that at the profit maximising output involves producing 10,000 units of X, then having 1 extra labour hour cannot be used to produce more X’s (because X has to be less that or equal to 10,000). So 1 extra hour can only be used to produce more Y’s which will result in extra contribution of $6/4 = $1.50.
Second question:
In this question, there are only two constraints and no limits on the maximum production of either product. Therefore you have to re-solve the optimal solution with 10,001 hours of labour instead of 10,000. The solution is as per the answer in the Revision Kit.
Have you watched my free lectures on linear programming? The lectures are a complete free course for Paper PM and cover everything needed to be able to pass the exam well.
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