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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 per unit Product y per unit Total available per period
Directs labour hours 2 hours 4 hours 10000hours
Material x 4kg 2kg 14000kg
Contribution per unit 12 18
The profit-maximising level of output and sales is 3000 units of product x and 1000 units of product y.
What is the shadow price of a direct labour hour?
Can the direct labour hours equation and x =3000 units equation be used to solve this problem. If not why not
Also why can not the direct labour hours equation and y= 1000 units equation be used to solve this problem.
Also can the direct labour hours equation and the total contribution equation be used to solve this problem instead of using the material constraint equation.
Why only material constraint equation has to be used to solve this problem
When I used x = 3000 units equation and the direct labour hours equation I got a shadow price of 4.5.
When I used y = 1000 units equation and the direct labour hours equation I got a shadow price of 6
When I used the total contribution equation and the direct labour hours equation I got a shadow price of zero. Why is it zero?
Also is the shadow price of 4.5 or 6 or 0 correctThere is no point in continuing to ask me questions like this if you are not prepared to watch my lectures. You are wasting my time and you are wasting your own time, since you clearly do not understand linear programming.
How on earth can x remain at 3,000 or y remain at 1,000 if there is one extra hour of labour? That would make no sense at all.
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