What is the dual price for finishing hours? interpret the value? If carpenters a
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Question
What is the dual price for finishing hours? interpret the value?
If carpenters are willing to work overtime, what is the most that they should be paid?
How much would you be willing to pay for extra lumber?
How much revenue could you generate if you had 21 finishing hours? 23 hours?
If you could get $34 for tables, how would your optimal solution change?
The Dakota Furniture Company manufactures desks, tables and chairs. The manufacture of each type of furniture requires lumber and two types of skilled labor: finishing and carpentry. The amount of each resource needed to make each type of furniture is given in the table below. Desk Table Kesource Chair Lumber (bd ft) inishing hrs Carpentry hrs 1.5 0.5 1.5 At present, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are available. A desk sells for $60, a table for $30, and a chair for $20. Dakota believes that the demand for desks and chairs is unlimited, but at most five tables can be sold. The linear programming model that can be used to maximize the company's total profits is given below: Let, XI = # Desks, X2 = # Tables, X3 = # Chairs, Max 60x1 30x2+20x3 S.T 8x1 + 6x2 + x3Explanation / Answer
What is the dual price for the finishing hours? interpret the value.
Dual price is $10. One hour of extra capacity in finishing will increase the revenue by $10 within a range of [16, 24] for the total capacity.
If carpenters are willing to work overtime, what is the most that they should be paid?
Dual price for the carpentry hrs. is also $10. This means that one hour of extra capacity in carpentry will increase the revenue by $10. Therefore, it is only economical to go for such overtime if the pay per overtime hour is less than $10.
How much would you be willing to pay for extra lumber?
Dual price for the lumber is $0. This means that one hour of extra capacity in lumber will increase the revenue by nothing as there is already a slack of 24 board feet. Therefore, we should not pay for extra lumber.
How much revenue could you generate if you had 21 finishing hours? 23 hours?
Present Revenue at optimality = 60 x 2 + 30 x 0 + 20 x 8 = $280
Dual price = $10
So, for 21 finishing hours, the revenue would be $280 + 1 x $10 = $290
for 23 finishing hours, the revenue would be $280 + 3 x $10 = $310
If you could get $34 for tables, how would your optimal solution change?
No change would happen as the reduced cost for the tables is $5. had it been $35 or more, the optimality would have changed.
If you could charge $18 for chairs, how would your optimal solution change?
The lower bound is $15. The upper bound is $22.5 As $18 remains within this range, no change will be observed is the optimal solution. Though, objective function will change as 60 x 2 + 30 x 0 + 18 x 8 = $264
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